This Week's Finds in Mathematical Physics

John Baez

Many of the papers I review are available on preprint archives such as hep-th, gr-qc, and the math preprint archives. If you click on the number of one of these papers, such as hep-th/9301028, a magic carpet will carry you to a place where you can read an abstract of the paper, and download it if you like. Click here for more information on how to get preprints electronically.

week1

1. Syzygies among elementary string interactions in 2+1 dimensions, by J. Scott Carter and Masahico Saito, Lett. Math. Phys. 23 (1991), 287-300.

   On formulations and solutions of simplex equations, by J. Scott Carter and Masahico Saito, Intern. J. of Mod. Phys. A., 11 (1996) 4453-4463.

   A diagrammatic theory of knotted surfaces, by J. Scott Carter and Masahico Saito, in Quantum Topology, eds. Randy Baadhio and Louis Kauffman, World Science Publishing, Singapore, 1993, 91-115.

   Reidemeister moves for surface isotopies and their interpretations as moves to movies, by J. Scott Carter and Masahico Saito, Journal of Knot Theory and its Ramifications 2 (1993), 251-284.

2. Knot theory and quantum gravity in loop space: a primer, by Jorge Pullin, to appear in "Proc. of the Vth Mexican School of Particles and Fields," ed. J. L. Lucio, World Scientific, Singapore, now available as hep-th/9301028.

3. Time, measurement and information loss in quantum cosmology, by Lee Smolin, preprint now available as gr-qc/9301016.

week2

1. Link invariants for intersecting loops, by Daniel Armand Ugon, Rodolfo Gambini, and Pablo Mora, October 1992 preprint, available from Gambini, Instituto de Fi'sica, Facultad de Ciencias, Trista'n Narvaja 1674, Montevideo, Uruguay.

2. New points of view in knot theory, by Joan Birman, preprint, to appear in the Bulletin of the AMS.

3. Link polynomials and a graphical calculus, by Louis Kauffman and P. Vogel, Jour. of Knot Theory and its Ramifications, 1 (1992), 59-104.

4. Categorical physics, by Louis Crane, preprint available as hep-th/9301061 in amstex.

   A Categorical construction of 4d topological quantum field theories, by Louis Crane and David Yetter, preprint available as hep-th/9301062.

   Hopf Categories and their representations, Louis Crane and Igor Frenkel, draft version.

   Categorification and the construction of topological quantum field theory, Louis Crane and Igor Frenkel, draft version.

5. The origin of time asymmetry, by S W Hawking, R Laflamme and G W Lyons, preprint available as gr-qc/9301017, in tex.

week3

1. On the Vassiliev Knot Invariants by Dror Bar-Natan, Harvard University ``pre-preprint.''

2. Mathematical problems of non-perturbative quantum general relativity, by Abhay Ashtekar, lectures delivered at the 1992 Les Houches summer school on Gravitation and Quantization, December 2, 1992, available as Syracuse University physics preprint SU-GP-92/11-2.

week4

1. Self-organized criticality in Monte Carlo simulated ecosystems, by R. Sole, D. Lopez, M. Ginovart and J. Valls, Phys. Lett. A172 (1992), p. 56.

2. There are no quantum jumps, nor are there particles!, by H. D. Zeh, Phys. Lett. A173, p. 189

3. Braided monoidal 2-categories, 2-vector spaces and Zamolodchikov tetrahedra equations, by M. M. Kapranov and V. A. Voevodsky. Preliminary incomplete version, September 1991. (Kapranov is at kapranov@chow.math.nwu.edu, and Voevodsky is at vladimir@math.ias.edu.)

week5

1. Indecomposable restricted representations of quantum sl_2, Vyjanathi Chari and Alexander Premet, University of California at Riverside preprint.

2. Representations of the quantized function algebras, 2-categories and Zamolodchikov tetrahedra equations, by David Kazhdan and Iakov Soibelman, Harvard University preprint.

3. A note on simplicial dimension shifting, Adrian Ocneanu, preprint available as hep-th/9302028.

4. The new configuration space for gravity: the spectrum of the algebra of SL(2,C)-holonomy functionals, by Abhay Ashtekar and Jerzy Lewandowski, draft version.

week6

1. Quantum cosmology, talk given at Texas/Pascos 1992 at Berkeley by Alexander Vilenkin, preprint available as gr-qc/9302016

2. Finite, diffeomorphism invariant observables in quantum gravity, by Lee Smolin, preprint available as gr-qc/9302011.

week7

1. Mathematical problems of non-perturbative quantum general relativity (lectures delivered at the 1992 Les Houches summer school on Gravitation and Quantization), by Abhay Ashtekar, 87 pp, available as gr-qc/9302024.

2. Lectures on Non-perturbative Canonical Gravity, by Abhay Ashtekar, World Scientific Press, 1991. (ISBN 981-02-0573-2 or for paperback, ISBN 981-02-0574-0. This can be ordered by calling World Scientific at 1-800-227-7562.)

3. We are not stuck with gluing, by David Yetter and Louis Crane, preprint available as hep-th/9302118, 2 pages.

4. The initial value problem in light of Ashtekar's variables, by R. Capovilla, J. Dell and T. Jacobson, preprint available as gr-qc/9302020, 15 pages.

5. Combinatorial expression for universal Vassiliev link invariant, by Sergey Piunikhin, preprint available as hep-th/9302084

week8

1. Map coloring and the vector cross product, by Louis Kauffman, J. Comb. Theory B, 48 (1990) 45.

   Map coloring, 1-deformed spin networks, and Turaev-Viro invariants for 3-manifolds, by Louis Kauffman, Int. Jour. of Mod. Phys. B, 6 (1992) 1765 - 1794.

   An algebraic approach to the planar colouring problem, by Louis Kauffman and H. Saleur, in Comm. Math. Phys. 152 (1993), 565-590.

2. Knots and physics, by Louis Kauffman, Proc. Symp. Appl. Math. 45 (1992), 131-246.

   Spin networks, topology and discrete physics, by Louis Kauffman, University of Illinois at Chicago preprint.

   Vassiliev invariants and the Jones polynomial, by Louis Kauffman, University of Illinois at Chicago preprint.

   Gauss codes and quantum groups, by Louis Kauffman, University of Illinois at Chicago preprint.

   Fermions and link invariants, by Louis Kauffman and H. Saleur, Yale University preprint YCTP-P21-91, July 5, 1991.

   State models for link polynomials, by Louis Kauffman, L'Enseignement Mathematique, 36 (1990), 1 - 37.

   The Conway polynomial in R^3 and in thickened surfaces: a new determinant formulation, by F. Jaeger, Louis Kauffman and H. Saleur, preprint.

week9

1. Surgical invariants of four-manifolds, by Boguslaw Broda, preprint available as hep-th/9302092.

   Reshetikhin-Turaev and Crane-Kohno-Kontsevich 3-manifold invariants coincide, by Sergey Piunikhin, preprint, 1992. (Piunikhin is at serguei@math.harvard.edu.)

   A link calculus for 4-manifolds, by E. Cesar de Sa, in Topology of Low-Dimensional Manifolds, Proc. Second Sussex Conf., Lecture Notes in Math., vol. 722, Springer, Berlin, 1979, pp. 16-30,

   A note on 4-dimensional handlebodies, by F. Laudenbach and V. Poenaru, Bull. Math. Soc. France 100 (1972), pp. 337-344,

2. Minisuperspaces: symmetries and quantization, by Abhay Ashtekar, Ranjeet S. Tate and Claes Uggla Syracuse University preprint SU-GP-92/2-5, 14 pages, available as gr-qc/9302026

   Minisuperspaces: observables and quantization, Abhay Ashtekar, Ranjeet S. Tate and Claes Uggla Syracuse University preprint SU-GP-92/2-6, 34 pages, available as gr-qc/9302027

3. Unique determination of an inner product by adjointness relations in the algebra of quantum observables, by Alan D. Rendall, Max-Planck-Institut fuer Astrophysik preprint, 10 pages, available as gr-qc/9303026.

4. Thawing the frozen formalism: the difference between observables and what we observe, by Arlen Anderson, preprint available as gr-qc/9211028.

5. Canonical Quantum Gravity and the Problem of Time, Chris J. Isham, 125 pages, preprint available as gr-qc/9210011.

6. The extended loop group: an infinite dimensional manifold associated with the loop space, by Cayetano Di Bartolo, Rodolfo Gambini and Jorge Griego, 42 pages, preprint available as gr-qc/9303010.

week10

1. Beyond Einstein - is space loopy? by Marcia Bartusiak, Discover, April 1993.

2. Vassiliev invariants contain more information than all knot polynomials, by Sergey Piunikhin, preprint. (Piunikhin is at serguei@math.harvard.edu)

   Turaev-Viro and Kauffman-Lins invariants for 3-manifolds coincide, by Sergey Piunikhin, Journal of Knot Theory and its Ramifications, 1 (1992) 105 - 135.

   Different presentations of 3-manifold invariants arising in rational conformal field theory, by Sergey Piunikhin, preprint.

   Weights of Feynman diagrams, link polynomials and Vassiliev knot invariants, by Sergey Piunikhin, preprint.

   Reshetikhin-Turaev and Crane-Kohno-Kontsevich 3-manifold invariants coincide, by Sergey Piunikhin, preprint.

3. Bibliography of publications related to classical and quantum gravity in terms of the Ashtekar variables, by Bernd Bruegmann, 14 pages, available as gr-qc/9303015.

4. Surgical invariants of four-manifolds, by Boguslaw Broda, preprint available as hep-th/9302092. (Revisited - see "week9")

week11

1. Unique determination of an inner product by adjointness relations in the algebra of quantum observables, by Alan D. Rendall, 10 pages, now available as gr-qc/9303026.

2. An algebraic approach to the quantization of constrained systems: finite dimensional examples, by Ranjeet S. Tate, Syracuse University physics department PhD dissertation, August 1992, SU-GP-92/8-1. (Tate is now at rstate@cosmic.physics.ucsb.edu, but please don't ask him for copies unless you're pretty serious, because it's big.)

week12

1. Canonical quantum gravity, by Karel Kuchar, preprint available as gr-qc/9304012.

2. 2-categories and 2-knots, by John Fischer, preprint, last revised Feb. 6 1993. (Fischer is at fischer-john@math.yale.edu)

3. A new discretization of classical and quantum general relativity, by Mark Miller and Lee Smolin, 22 pages, preprint available as gr-qc/9304005.

4. Higher algebraic structures and quantization, by Dan Freed, preprint, December 18, 1992, available as hep-th/9212115; see also week48.

week13

1. Elliptic Curves by Anthony W. Knapp, Mathematical Notes, Princeton University Press, 1992.

2. Elliptic Functions by Serge Lang, Springer-Verlag, 2nd edition, 1987.

3. Elliptic Curves by Dale Husemoeller, Springer-Verlag, 1987.

4. Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli spaces, by Jim Stasheff, preprint available as hep-th/9304061.

5. A geometrical presentation of the surface mapping class group and surgery, by Sergey Matveev and Michael Polyak, preprint.

6. Invariants of 3-manifolds and conformal field theories, by Micheal Polyak, preprint.

week14

1. Skein theory and Turaev-Viro invariants, by Justin Roberts, Pembroke College preprint, April 14, 1993 (Roberts is at J.D.Roberts@pmms.cam.ac.uk)

2. The basis of the Ponzano-Regge-Turaev-Viro-Ooguri model is the loop representation basis, by Carlo Rovelli, 16 pages, preprint available as hep-th/9304164.

3. Diffeomorphism-invariant generalized measures on the space of connections modulo gauge transformations, by John Baez, to appear in the proceedings of the Conference on Quantum Topology, Manhattan, Kansas, May 8, 1993, also available as state.tex.

4. Completeness of Wilson loop functionals on the moduli space of SL(2,C) and SU(1,1)-connections, Abhay Ashtekar and Jerzy Lewandowski, 7 pages, preprint available as gr-qc/9304044.

5. An algebraic approach to the quantization of constrained systems: finite dimensional examples, by Ranjeet S. Tate, (Ph.D. Dissertation, Syracuse University), 124 pages, LaTeX (run thrice before printing), available as gr-qc/9304043.

6. SU(2) QCD in the path representation, by Rodolfo Gambini and Leonardo Setaro, 37 pages, preprint available as hep-lat/9305001.

week15

1. Closed string field theory - an introduction, by Barton Zwiebach, preprint available as hep-th/9305026 (requires the phyzzx macros to print; these macros are also available from hep-th; see below).

2. Two-dimensional Yang-Mills theories are string theories, by S.G. Naculich, H.A. Riggs, and H.J. Schnitzer, 14 pages, preprint available as hep-th/9305097.

week16

1. Structure of topological lattice field theories in three dimensions, by Stephen-wei Chung, Masafumi Fukuma and Alfred Shapere, preprint, available as hep-th/9305080 (make sure to get the pictures if possible)!

2. C. Bachas and P. M. S. Petropoulos, Comm. Math. Phys. 152 (1993) 191.

3. Lattice topological field theory in two-dimensions, by M. Fukuma, S. Hosono and H. Kawai, preprint available as hep-th/921254, now in print in Comm. Math. Phys. 161 (1994) 157-175.

4. Six ways to quantize (2+1)-dimensional gravity, by Steven Carlip (carlip@nsfitp.itp.ucsb.edu), 21 pages, preprint available as gr-qc/9305020.

5. An illustration of 2+1 gravity loop transform troubles, by Donald Marolf (MAROLF@SUHEP.PHY.SYR.EDU), 6 pages, preprint available as gr-qc/9305015.

6. G. Ponzano and T. Regge: in Bloch, F. (ed.), Spectroscopic and Group Theoretical Methods in Physics, Amsterdam: North-Holland 1968.

7. 2+1 dimensional gravity as an exactly soluble system, by E. Witten, Nucl. Phys. 311 (1988), 46-78.

8. State sum invariants of 3-manifolds and quantum 6j-symbols, by V. G. Turaev and O. Y. Viro, Topology 31 (1992), 865.

9. H. Ooguri, Mod. Phys. Lett. A7 (1992), 2799.

10. Actions for gravity, with generalizations: a review, by Peter Peldan (tfepp@fy.chalmers.se), 61 pages, preprint available as gr-qc/9305011

week17

1. ``Theoretical Mathematics'': Toward a cultural synthesis of mathematics and theoretical physics, by Arthur Jaffe and Frank Quinn, to appear in the July 1993 Bulletin of the AMS (available by gopher at e-math.ams.com, but don't ask me how).

2. New Scientific Applications of Geometry and Topology, ed. DeWitt L. Sumner, Proc. Symp. Appl. Math. 45, published by the AMS.

3. Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, by Louis Kauffman and Sostenes Lins, to be published by Princeton U. Press.

4. 12j-symbols and four-dimensional quantum gravity, by M. Carfora, M. Martellini (martellini@milano.infn.it), and A. Marzuoli, Dipartimento di Fisica, Universita di Roma "La Sapienza" preprint.

5. Selected topics in quantum groups, by Y. S. Soibelman (soibel@math.harvard.edu), Lectures for the European School of Group Theory, Harvard University preprint.

6. Braids and movies, by J. Scott Carter (carter@mathstat.usouthal.edu) and Masahico Saito, preprint.

7. Combinatorial Invariants from Four Dimensional Lattice Models: II, by Danny Birmingham and Mark Rakowski, preprint available as hep-th/9305022.

8. A note on the four-dimensional Kirby calculus, by Boguslaw Broda, preprint, 5 pages, preprint available as hep-th/9305101.

9. Solutions to the Wheeler DeWitt constraint of canonical gravity coupled to scalar matter fields, by H.-J. Matschull, preprint available as gr-qc/9305025.

week18

1. Strings, loops, knots, and gauge fields, by John Baez, preprint available as hep-th/9309067, 34 pages. Also available in LaTeX as string.tex.

week19

1. Evaluating the Crane-Yetter Invariant, by Louis Crane, Louis H. Kauffman, David N. Yetter, 4 pages, preprint available as hep-th/9309063.

2. On the Classicality of Broda's SU(2) Invariants of 4-Manifolds, by Louis Crane, Louis H. Kauffman, David N. Yetter, 4 pages, preprint available as hep-th/9309102.

3. Exactly soluble diffeomorphism-invariant theories, by Gary Horowitz, Comm. Math. Phys., 125 (1989) 417-437.

week20

1. John H. Conway and Neil J. A. Sloane, Sphere Packings, Lattices and Groups, second edition, Grundlehren der mathematischen Wissenschaften 290, Springer-Verlag, 1993.

2. Igor Frenkel, James Lepowsky, and Arne Meurman, Vertex Operator Algebras and the Monster, Academic Press, New York, 1988.

week21

1. Knotted surfaces, braid movies, and beyond, by J. Scott Carter and M. Saito, to appear in Knots and Quantum Gravity, ed. John Baez, Oxford U. Press.

2. How Surfaces Intersect in Space: An Introduction to Topology, by J. Scott Carter, World Scientific Press, Singapore 1993. ISBN 981-02-1050

3. A Topological Picturebook, by George Francis, Springer-Verlag, 1987.

week22

1. The Four-Color Problem: Assault and Conquest, by Thomas L. Saaty and Paul C. Kainen, McGraw-Hill, 1977, ISBN 0-07-054382-8.

2. Map coloring and the vector cross product, by Louis Kauffman, J. Comb. Theory B, 48 (1990) 45.

   Map coloring, 1-deformed spin networks, and Turaev-Viro invariants for 3-manifolds, by Louis Kauffman, Int. Jour. of Mod. Phys. B, 6 (1992) 1765 - 1794.

   An algebraic approach to the planar colouring problem, by Louis Kauffman and H. Saleur, Yale University preprint YCTP-P27-91, November 8, 1991.

3. Every Planar Map is Four Colorable, by Kenneth Appel and Wolfgang Haken, Contemporary Mathematics (American Mathematical Society), v. 98, 1989.

4. Applications of negative dimensional tensors, by Roger Penrose, in Combinatorial Mathematics and its Applications, ed. D. J. A. Welsh, Academic Press, 1971.

week23

1. Topological quantum invariants and the Andrews-Curtis conjecture (Progress report), by Frank Quinn, preprint, Sept. 1993.

2. Lectures on axiomatic topological quantum field theory, by Frank Quinn, to appear in the proceedings of the Park City Geometry Institute.

3. On the Andrews-Curtis conjecture and related problems, by Wolfgang Metzler, in Combinatorial Methods in Topology and Algebraic Geometry, Contemporary Mathematics 44, AMS, 1985.

4. Elements of Homotopy Theory, by George W. Whitehead, Springer-Verlag, Berlin, 1978. ISBN 0-387-90336-4

5. S. Gelfand and D. Kazhdan, Examples of tensor categories, Invent. Math. 109 (1992) 595-617.

6. Knots and Quantum Gravity, ed. John Baez, Oxford University Press, Oxford, 1994. ISBN 0-19-853490-6. (This can be ordered by calling 0536 454 534 in the UK, or + 44 536 454 534 outside the UK.)

   The loop formulation of gauge theory and gravity, by Renate Loll

   Representation theory of analytic holonomy C* algebras, by Abhay Ashtekar and Jerzy Lewandowski (currently available as gr-qc/9311010)

   The Gauss linking number in quantum gravity, by Rodolfo Gambini and Jorge Pullin (currently available as gr-qc/9310025)

   Vassiliev invariants and the loop states in quantum gravity, by Louis H. Kauffman (soon to be on gr-qc)

   Geometric structures and loop variables in (2+1)-Dimensional gravity, by Steven Carlip (currently available as gr-qc/9309020)

   From Chern-Simons to WZW via path integrals, by Dana S. Fine

   Topological field theory as the key to quantum gravity, by Louis Crane (currently available as hep-th/9308126)

   Strings, loops, knots and gauge gields, by John Baez (currently available as hep-th/9309067 and also at string.tex).

   BF Theories and 2-knots, by Paolo Cotta-Ramusino and Maurizio Martellini

   Knotted surfaces, braid movies, and beyond, by J. Scott Carter and Masahico Saito

week24

1. Prima facie questions in quantum gravity, by Chris Isham, lecture at Bad Honeff, September 1993, preprint available as gr-qc/9310031.

2. Lectures on 2d gauge theories: topological aspects and path integral techniques, by Matthias Blau and George Thompson, 70 pages, preprint available as hep-th/9310144.

3. Semi-classical limits of simplicial quantum gravity, by J. W. Barrett and T. J. Foxon, preprint available as gr-qc/9310016.

4. Wave function of the universe, by J. B. Hartle and S. W. Hawking, Phys. Rev. D28 (1983), 2960.

5. Generalized measures in gauge theory, by John Baez, available as hep-th/9310201. Also available as conn.tex.

week25

1. Loop Spaces, Characteristic Classes and Geometric Quantization, by Jean-Luc Brylinski, Birkhauser, Boston, 1993. ISBN 0-176-3644-7

2. Quantization and unitary representations, by Bertram Kostant, in Lectures in Modern Analysis and Applications III, Springer-Verlag Lecture Notes in Mathematics 170 (1970), 87-208.

3. Vortices in He II, current algebras and quantum knots, by M. Rasetti and T. Regge, Physica 80A (1975) 217-233.

4. A geometric approach to quantum vortices, by V. Penna and M. Spera, J. Math. Phys. 30 (1989), 2778-2784.

5. Higher algebraic structures and quantization, by Dan Freed, preprint, December 18, 1992, available as hep-th/9212115.

6. Representation Theory of Analytic Holonomy C* Algebras, by Abhay Ashtekar and Jerzy Lewandowski, to appear in Knots and Quantum Gravity, ed. J. Baez, 42 pages, currently available as gr-qc/9311010.

week26

1. Cosmology, time's arrow, and that old double standard, by Huw Price, 26 pages, available as gr-qc/9310022. (Written for Time's Arrows Today Conference, UBC, Vancouver, June 1992; forthcoming in Savitt, S., ed., "Time's Arrows Today," Cambridge University Press, 1994.)

2. The Physical Basis of the Direction of Time, by H. D. Zeh, Second Edition, Springer-Verlag, 1992. ISBN 3-540-54884-X or 0-387-54884-X

3. Chromodynamics and gravity as theories on loop space, by R. Loll, 56 pages, 10 figures (postscript, compressed and uuencoded), preprint available as hep-th/9309056.

4. Intersecting braids and intersecting knot theory, by Daniel Armand-Ugon, Rodolfo Gambini and Pablo Mora, Latex 14 pages (6 figures included), available as hep-th/9309136.

week27

1. Conceptual Problems of Quantum Gravity, edited by Abhay Ashtekar and John Stachel, based on the proceedings of the 1988 Osgood Hill Conference, 15-19 May 1988, Birkhaueser, Boston, 1991.

2. Quantum measurements and the environment-induced transition from quantum to classical, by Wojciech H. Zurek, the volume above.

   Loss of quantum coherence for a damped oscillator, by W. G. Unruh, the volume above.

3. Is there incompatibility between the ways time is treated in general relativity and in standard quantum mechanics?, by Carlo Rovelli, the volume above.

   The problem of time in canonical quantization of relativistic systems, by Karel V. Kuchar, the volume above.

   Time and prediction in quantum cosmology, by James B. Hartle, the volume above.

   Space and time in the quantum universe, by Lee Smolin, the volume above.

4. Old problems in the light of new variables, by Abhay Ashtekar, the volume above.

   Loop representation in quantum gravity, by Carlo Rovelli, the volume above.

   Nonperturbative quantum gravity via the loop representation, by Lee Smolin, the volume above.

week28

1. An Introduction to Teichmueller spaces, by Y. Imayoshi and M. Taniguchi, Springer-Verlag, 1991, ISBN 4-431-70088-9.

2. An introduction to the moduli space of curves, by Joe Harris, in Mathematical Aspects of String Theory (proceedings of a conference at UC San Diego in 1986), ed. S. T. Yau, World Scientific Press, 1987, ISBN 9971-50-274-7.

3. The cohomology of the moduli space of curves, by John L. Harer, in Theory of Moduli (lectures given at the 3rd 1985 session of C.I.M.E. at Mondecatini Terme, Italy), ed. E. Sernesi, Springer-Verlag Lecture Notes in Mathematics 1337, 1988, ISBN 0-387-50080-4.

4. A presentation of the mapping class group of a closed, orientable surface, by A. Hatcher and W. Thurston, Topology 19 (1980), 221-237.

5. A simple presentation for the mapping class group of an orientable surface, Israel J. Math. 45 (1983), 157-174.

6. Braids, Links, and Mapping Class Groups, by Joan S. Birman, Annals of Mathematics Studies no. 82, Princeton University Press, 1974.

7. Universal constructions in Teichmueller theory, by R. C. Penner, Adv. Math. 98 (1993), 143-215.

8. Classical and quantum conformal field theory, by G. Moore and S. Seiberg, Comm. Math. Phys. 123 (1989) 177-254

9. 2-d physics and 3-d topology, by Louis Crane, Comm. Math. Phys. 135 (1991) 615-640.

week29

1. On algebras and triangle relations, by Ruth J. Lawrence, to appear in Proc. Top. & Geom. Methods in Field Theory (1992), eds. J. Mickelsson and O. Pekonen, World Scientific, Singapore.

   A presentation for Manin and Schechtman's higher braid groups, by R. J. Lawrence, available as MSRI preprint 04129-91.

   Triangulations, categories and extended topological field theories, by R. J. Lawrence, in Quantum Topology, eds L. Kauffman and R. Baadhio, World Scientific, Singapore, 1993.

   Algebras and triangle relations, by R. J. Lawrence, Harvard U. preprint.

2. Coherence for tricategories, by R. Gordon, A. J. Power, and R. Street, preprint, 81 pages.

3. Formal Category Theory: Adjointness for 2-categories, by John W. Gray, Lecture Notes in Mathematics 391, Springer-Verlag, New York, 1974. ISBN 3-540-06830-9.

   Coherence for the tensor product of 2-categories, and braid groups, in Algebras, Topology, and Category Theory, eds. A. Heller and M. Tierney, Academic Press, New York, 1976, pp. 63-76.

4. On pentagon and tetrahedron equations, by J. M. Maillet, preprint available as hep-th/9312037.

5. Homologically twisted invariants related to (2+1)- and (3+1)-dimensional state-sum topological quantum field theories, by David N. Yetter, preprint, 6 pages, available as hep-th/9311082.

week30

1. QED and the Men Who Made It: Dyson, Feynman, Schwinger and Tomonaga, by Silvan S. Schweber, Princeton Series in Physics, Princeton U. Press, 784 pages, available May 1994. Paperback: ISBN 0-691-03327-3 ($39.50).

2. The Music of the Heavens: Kepler's Harmonic Astronomy, by Bruce Stephenson, Princeton U. Press, 296 pages, available July 1994. Cloth: ISBN 0-691-03439-7 ($39.50).

   Kepler's Physical Astronomy, by Bruce Stephenson, Princeton U. Press, 218 pages, paperback available June 1994. ISBN 0-691-03652-7 ($14.95).

3. Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, by Louis Kauffman and Sostenes Lins, Annals of Mathematics Studies No. 133, Princeton U. Press, 304 pages, available July 1994. Paperback: ISBN 0-691-03640-3 ($22.50).

4. The physical hamiltonian in quantum gravity, by C. Rovelli and L. Smolin, 11 pages, preprint available as gr-qc/9308002.

   Fermions in quantum gravity, by H. A. Morales-Tecotl and C. Rovelli, 37 pages, preprint available as gr-qc/9401011.

5. Extended loops: a new arena for nonperturbative quantum gravity, by C. Di Bartolo, R. Gambini, J. Griego and J. Pullin, 12 pages, preprint available in Revtex form as gr-qc/9312029.

6. Ashtekar variables in classical general relativity, by Domenico Giulini, 43 pages, preprint available as gr-qc/9312032.

week31

1. Possible implications of the quantum theory of gravity, by Louis Crane, 5 pages, preprint available as hep-th/9402104.

2. S. W. Hawking, Phys. Rev. D13, 191 (1976).

3. Do black holes destroy information? by J. Preskill, Caltech report CALT-68-1819, available as hep-th/9209058, Sept. 1992.

4. Black hole information, by Don Page, review lecture to be published in Proceedings of the 5th Canadian Conference on General Relativity and Relativistic Astrophysics, University of Waterloo, 13--15 May, 1993}, edited by R. B. Mann and R. G. McLenaghan (World Scientific, Singapore, 1994) now available as hep-th/9305040.

5. Some speculations about black hole entropy in string theory, Leonard Susskind, 11 pages, preprint available as hep-th/9309145.

   Black hole entropy in canonical quantum gravity and superstring theory, by L. Susskind and J. Uglum, 29 pages, available as hep-th/9401070.

6. Black hole evaporation without information loss, by C.R. Stephens, G. 't Hooft and B. F. Whiting, 35 pages, 3 figures in postscript, preprint available as gr-qc/9310006.

7. Complementarity in wormhole chromodynamics, by Hoi-Kwong Lo, Kai-Ming Lee, and John Preskill, 12 pages and 2 figures, phyzzx macros required, available as hep-th/9308044.

8. "No hair" theorems -- folklore, conjectures, results, by Piotr T. Chrusciel, Garching preprint MPA 792, 30 pages available as gr-qc/9402032.

9. On uniqueness in the large of solutions of Einstein's equations ("Strong cosmic censorship"), by Piotr T. Chrusciel, in Mathematical Aspects of Classical Field Theory, Contemp. Math. 132, eds. Gotay, Marsden and Moncrief, AMMS, Rhode Island, 1992, pp. 235-274.

week32

1. On quantum mechanics, by Carlo Rovelli, uuencoded PostScript file, 42 pages available as hep-th/9403015.

2. Adjointness relations as a criterion for choosing an inner product, by Alan Rendall, gr-qc/9403001.

3. Gromov-Witten classes, quantum cohomology, and enumerative geometry, by M. Kontsevich, Yu. Manin, hep-th/9402147.

week33

1. Gauge Fields, Knots and Gravity, by John Baez and Javier de Muniain, World Scientific Press. (ISBN 981-02-1729-3, or ISBN 981-02-2034-0 for paperback. This can be ordered by calling World Scientific at 1-800-227-7562.)

2. Quantum Theory: Concepts and Methods, by Asher Peres, Kluwer Academic Publishers, 1994, ISBN 0-7923-2549-4.

3. Loop representations, by Bernd Bruegmann, Max Planck Institute preprint, available as gr-qc 9312001.

4. The fate of black hole singularities and the parameters of the standard models of particle physics and cosmology, by Lee Smolin, preprint available as gr-qc/9404011.

week34

1. Algorithms for quantum computation: discrete log and factoring, extended abstract by Peter Shor.

2. Simulating physics with computers, by Richard Feynman, International Journal of Theoretical Physics, Vol. 21, nos. 6/7, pp. 467--488 (1982).

3. Quantum mechanical Hamiltonian models of Turing machines, by P. Benioff J. Stat. Phys., Vol. 29, pp. 515--546 (1982).

   Quantum theory, the Church--Turing principle and the universal quantum computer, by D. Deutsch, Proc. R. Soc. Lond., Vol. A400, pp. 96--117 (1985).

   Quantum computational networks, by D. Deutsch, Proc. R. Soc. Lond., Vol. A425, pp. 73--90 (1989).

   Rapid solution of problems by quantum computation, by D. Deutsch and R. Jozsa, Proc. R. Soc. Lond., Vol. A439, pp. 553--558 (1992).

   Quantum complexity theory, E. Bernstein and U. Vazirani, Proc. 25th ACM Symp. on Theory of Computation, pp. 11--20 (1993).

   The quantum challenge to structural complexity theory, A. Berthiaume and G. Brassard, Proc. 7th IEEE Conference on Structure in Complexity Theory (1992).

   Quantum circuit complexity, by A. Yao, Proc. 34th IEEE Symp. on Foundations of Computer Science, 1993.

4. The Chern-Simons invariant as the natural time variable for classical and quantum cosmology, by Lee Smolin and Chopin Soo, 16 pages, preprint available as gr-qc/9405015.

5. Symplectic geometry, a series of lectures by Mikhail Gromov, compiled by Richard Brown, edited by Robert Miner (lena@math.umd.edu).

week35

1. Pursuing stacks (A la poursuite des champs), 1983 letter from Alexandre Grothendieck to Daniel Quillen, 593 pages, apparently available only from someone who wants to copy 593 pages for you - i.e., not me!

2. J. Benabou, Introduction to bicategories, Lect. Notes in Math., vol. 47, Berlin, Springer-Verlag, 1968, pp. 1-71.

3. Selected bibliography on higher-dimensional algebra.

week36

1. Three-dimensional BF theories and the Alexander-Conway invariant of knots, by A. S. Cattaneo, P. Cotta-Ramusino, and M. Martellini; 32 pages (figures available upon request), available as hep-th/9407070.

2. B^F theory and flat spacetimes, by Henri Waelbroeck, 21 pages, preprint available as gr-qc/9311033.

3. A Hamiltonian formulation of topological gravity, by Henri Waelbrock and J. A. Zapata, 15 pages, preprint available as gr-qc/9311035.

4. Topological Yang-Mills symmetry, by L. Baulieu and I. M. Singer, Nucl. Phys. (Proc. Suppl.) B5 (1988) 12-19.

5. On quantum gauge theories in two dimensions, by Edward Witten, Comm. Math. Phys. 141 (1991) 153-209.

6. Topological gauge theories of antisymmetric tensor fields, by M. Blau and G. Thompson, Ann. Phys. 205 (1991) 130-172.

week37

1. L. Lindblom, Superfluid hydrodynamics and the stability of rotating neutron stars, talk at MG7 meeting, Monday July 5, Stanford University.

2. Abhay Ashtekar, Mathematical developments in quantum general relativity, a sampler, talk at MG7 meeting, Tuesday July 6, Stanford University. Available as gr-qc/9411055.

week38

1. Topological quantum field theories from generalized 6j-symbols, B. Durhuus, H. P. Jakobsen and R. Nest, Reviews in Math. Physics 5 (1993), 1-67.

2. Spin networks, Turaev-Viro theory and the loop representation, by Timothy J. Foxon, preprint available as gr-qc/9408013.

3. Involutory Hopf algebras and three-manifold invariants, by Greg Kuperberg, Internat. Jour. Math 2 (1991), 41-66.

   A definition of #(M,H) in the non-involutory case, by Greg Kuperberg, unpublished.

4. Spherical categories, by John W. Barrett and Bruce W. Westbury, preprint available as hep-th/9310164.

   Invariants of piecewise-linear 3-manifolds, by John W. Barrett and Bruce W. Westbury, Trans. Amer. Math. Soc. 348 (1996), 3997-4022, preprint available as hep-th/9311155.

   The equality of 3-manifold invariants, by John W. Barrett and Bruce W. Westbury, preprint available as hep-th/9406019.

5. Invariants of 3-Manifolds derived from finite dimensional Hopf algebras, by Louis H. Kauffman and David E. Radford, 33 pages, preprint available as hep-th/9406065.

6. Four dimensional topological quantum field theory, Hopf categories, and the canonical bases, by Louis Crane and Igor Frenkel, available as hep-th/9405183.

7. A manifestly gauge-invariant approach to quantum theories of gauge fields, by A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao, T. Thiemann, contribution to the Cambridge meeting proceedings, 27 pages, preprint available as hep-th/9408108.

   Topological measure and graph-differential geometry on the quotient space of connections, Jerzy Lewandowski, 3 pp., Proceedings of ``Journees Relativistes 1993'', 3 pages available as gr-qc/9406025.

   Integration on the space of connections modulo gauge transformations, Abhay Ashtekar, Donald Marolf, Jose Mourao, 18 pages, preprint available as gr-qc/9403042.

   New loop representations for 2+1 gravity, by A. Ashtekar and R. Loll, 28 pages, preprint available as gr-qc/9405031.

   Independent loop invariants for 2+1 gravity, by R. Loll, 2 figures, gr-qc/9408007.

   Generalized coordinates on the phase space of Yang-Mills theory, by R. Loll, J.M. Mour\~ao and J.N. Tavares, 11 pages, preprint available as gr-qc/9404060.

   The extended loop representation of quantum gravity, C. Di Bartolo, R. Gambini and J. Griego, 27 pages available as gr-qc/9406039.

   The constraint algebra of quantum gravity in the loop representation, by Rodolfo Gambini, Alcides Garat and Jorge Pullin, 18 pages in Revtex, available as gr-qc/9404059.

week39

1. Noncommutative Geometry, by Alain Connes, Academic Press, 640 pp., $59.95 (tentative), ISBN 0-12-185860-X. (Orders can be placed in the US by calling 1-800-321-5068.)

2. 2d Yang-Mills theory and topological field theory, by Gregory Moore, available as hep-th/9409044.

3. Strings and two-dimensional QCD for finite N, by J. Baez and W. Taylor, 19 pages available as hep-th/9401041, or in LaTeX as string2.tex. To appear in Nuc. Phys. B.

4. The symplectic nature of fundamental groups of surfaces, by W. Goldman, Adv. Math. 54 (1984), 200-225.

   Invariant functions on Lie groups and Hamiltonian flows of surface group representations, by W. Goldman, Invent. Math. 83 (1986), 263-302.

   Topological components of spaces of representations, by W. Goldman, Invent. Math. 93 (1988), 557-607.

5. "The Geometry and Physics of Knots," by Michael Atiyah, Cambridge U. Press, Cambridge, 1990.

6. Group cohomology construction of the cohomology of moduli spaces of flat connections on 2-manifolds, by Lisa C. Jeffrey, preprint available from Princeton U. Mathematics Department.

week40

1. Linear Logic, by Jean-Yves Girard, Theoretical Computer Science 50 (1987) pp. 1-102.

2. Linear logic for generalized quantum mechanics, by Vaughan Pratt, available in LaTeX format (compressed) by anonymous ftp from boole.stanford.edu, as the file pub/ql.tex.Z

3. Hopf algebras and linear logic, by Richard Blute, to appear in Mathematical Structures in Computer Science.

4. Linear logic, *-autonomous categories and cofree coalgebras, by R. A. G. Seely, in Categories in Computer Science and Logic, Contemp. Math. 92 (1989).

5. Quantales and (noncommutative) linear logic, by D. Yetter, Journal of Symbolic Logic 55 (1990), 41-64.

week41

1. The Statistical Mechanics of the (2+1)-Dimensional Black Hole, by Steve Carlip, 12 pages available as gr-qc/9409052.

2. Angular momentum; an approach to combinatorial space time, by Roger Penrose, in "Quantum Theory and Beyond," ed. T. Bastin, Cambridge University Press, Cambridge, 1971.

3. Conformal field theory, spin geometry, and quantum gravity, by Louis Crane, Phys. Lett. B259 (1991), 243-248.

4. Von Neumann algebra automorphisms and time-thermodynamics relation in general covariant quantum theories, by A. Connes and C. Rovelli, 25 pages in LaTex format available as gr-qc/9406019.

5. The affine symmetry of self-dual gravity, by Viqar Husain, 17 pages, preprint available as hep-th/9410072.

6. Knots and quantum gravity: progress and prospects, John Baez, 22 pages, preprint available as gr-qc/9410018.

7. "Matters of Gravity", a newsletter for the gravity community, Number 4, edited by Jorge Pullin, 24 pages, preprint available as gr-qc/9409004, or from WWW by http://www.phys.lsu.edu//mog/

week42

1. QCD and the string model, by Y. Nambu, Phys. Lett. B80 (1979) 372-376.

   Gauge fields as rings of glue, A. Polyakov, Nucl. Phys. B164 (1979) 171-188.

   The quantum dual string wave functional in Yang-Mills theories, by J. Gervais and A. Neveu, Phys. Lett. B80 (1979), 255-258.

   The interaction among dual strings as a manifestation of the gauge group, by F. Gliozzi and M. Virasoro, Nucl. Phys. B164 (1980), 141-151.

   Loop-space representation and the large-N behavior of the one-plaquette Kogut-Susskind Hamiltonian, A. Jevicki, Phys. Rev. D22 (1980), 467-471.

   Quantum chromodynamics as dynamics of loops, by Y. Makeenko and A. Migdal, Nucl. Phys. B188 (1981) 269-316.

   Loop dynamics: asymptotic freedom and quark confinement, by Y. Makeenko and A. Migdal, Sov. J. Nucl. Phys. 33 (1981) 882-893.

2. Conformal field theory, by Krzysztof Gawedzki, Seminaire Bourbaki, Asterisque 177-178 (1989), pp. 95-126.

3. Introduction to Superstrings, by Michio Kaku, New York, Springer-Verlag, 1988.

   String Fields, Conformal Fields, and Topology, by Michio Kaku, New York, Springer-Verlag, 1991.

4. Quantum background independence of closed string field theory, by Ashoke Sen and Barton Zwiebach, 60 pages, phyzzx.tex, MIT-CTP-2244, available as hep-th/9311009.

   Background independent algebraic structures in closed string field theory, by Ashoke Sen and Barton Zwiebach, phyzzx.tex, MIT-CTP-2346, available as hep-th/9408053.

5. Loop representation for quantum general relativity, by C. Rovelli and L. Smolin, Nucl. Phys. B331 (1990), 80-152.

6. Gauge dynamics in the C-representation, by R. Gambini and A. Trias, Nucl. Phys. B278 (1986) 436-448.

7. Infinite Loop Spaces, by J. F. Adams, Princeton U. Press, Princeton, NJ, 1978.

8. Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli spaces, by Jim Stasheff, available as hep-th/9304061.

9. Loop groups, by Andrew Pressley and Graeme Segal, Oxford University Press, Oxford, 1986.

10. A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces, Junichi Iwasaki, University of Pittsburgh, 11 pages, preprint available as gr-qc/9410010.

11. Lattice QCD as a theory of interacting surfaces, by B. Rusakov, TAUP-2204-94, 12 pages, preprint available as hep-th/9410004.

    U(N) Gauge Theory and lattice strings, by Ivan K. Kostov, 26 pages, 8 figures not included, available by mail upon request, T93-079 (talk at the Workshop on string theory, gauge theory and quantum gravity, 28-29 April 1993, Trieste, Italy), available as hep-th/9308158.

12. Chern-Simons-Witten theory as a topological Fermi liquid, by Michael R. Douglas, Rutgers University preprint RU-94-29, available as hep-th/9403119.

week43

1. Quantum theory of gravity, I-III by Bryce S. DeWitt, Phys. Rev. 160 (1967), 1113-1148, 162 (1967) 1195-1239, 1239-1256.

2. Coherent state transforms for spaces of connections, by Abhay Ashtekar, Jerzy Lewandowski, Donald Marolf, Jose Mourao and Thomas Thiemann, 38 pages, preprint available as gr-qc/9412014.

   Quantum geometrodynamics, by A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourao and T. Thiemann, in progress, to appear on gr/qc.

3. The Hamiltonian constraint in quantum gravity, M. Blencowe, Nucl. Phys. B341 (1990), 213-251.

   On the constraints of quantum gravity in the loop representation, Bernd Bruegmann and Jorge Pullin, Nucl. Phys. B390 (1993), 399-438.

   On the constraints of quantum general relativity in the loop representation, Bernd Bruegmann, Ph.D. Thesis, Syracuse University (May 1993).

4. State-sum invariants of manifolds, I, by Louis Crane, Louis H. Kauffman, and David N. Yetter, 46 pages, LaTeX (Sun release 4.1) source code produces many error messages, but a correct dvi-file, available as hep-th/9409167.

5. Spin networks in gauge theory, by John Baez, 19 pages, preprint available as gr-qc/9411007 or in LaTeX at spin.tex.

6. Discreteness of area and volume in quantum gravity, by Carlo Rovelli and Lee Smolin, 36 pages, preprint available as gr-qc/9411005.

week44

1. "The Geometry of Four-Manifolds," by Simon K. Donaldson and P. B. Kronheimer, Oxford University Press, Oxford, 1990.

   Polynomial invariants for smooth four-manifolds, by S. K. Donaldson, Topology 29 (1990), 257-315.

   "Instantons and Four-Manifolds," by Daniel S. Freed and Karen K. Uhlenbeck, Springer-Verlag, New York (1984).

   "Differential Topology and Quantum Field Theory," by Charles Nash, Academic Press, London, 1991.

2. Geometry of four dimensional manifolds, by Simon K. Donaldson, videocassette (ca. 60 min.), color, 1/2 in., American Mathematical Society, Providence RI, 1988.

3. "Spin Geometry," by H. Blaine Lawson, Jr. and Marie-Louise Michelson, Princeton U. Press, Princeton, 1989.

week45

1. The genus of embedded surfaces in the projective plane, by P. B. Kronheimer and T. S. Mrowka, 10 pages.

2. Monopoles and four-manifolds, by Edward Witten, in preparation.

   Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory, by Nathan Seiberg and Edward Witten, 45 pages, available as hep-th/9407087.

   Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD, by Nathan Seiberg and Edward Witten, 89 pages, available as hep-th/9408099.

week46

1. The speed of write, by Gary Stix, Scientific American, Dec. 1994, 106-111.

   Goodbye, Gutenberg, by Jacques Leslie, WiReD 2.10, Oct. 1994, available via WWW as http://www.hotwired.com/Lib/Wired/2.10/departments /electrosphere/ejournals.html

2. Monopoles and four-manifolds, by Edward Witten, preprint available as hep-th/9411102.

   The genus of embedded surfaces in the projective plane, by P. B. Kronheimer and T. S. Mrowka, preprint number #19941128001, available from the AMS preprint server under subject 57 in the Mathematical Reviews Subject Classification Scheme.

3. Spin networks in quantum gravity, by Carlo Rovelli and Lee Smolin, to appear.

4. Recent mathematical developments in quantum general relativity, by Abhay Ashtekar, 14 pages in TeX format available as gr-qc/9411055 (discussed in "week37").

   Coherent state transforms for spaces of connections, by Abhay Ashtekar, Jerzy Lewandowski, Donald Marolf, Jose Mourao and Thomas Thiemann, Jour. Funct. Analysis 135 (1996), 519-551, preprint available as gr-qc/9412014 (discussed in "week43")

5. Differential geometry on the space of connections via graphs and projective limits, by Abhay Ashtekar and Jerzy Lewandowski, Jour. Geom. and Phys. 17 (1995), 191-230, preprint available as hep-th/9412073.

6. Edge states in gravity and black hole physics, by A. P. Balachandran, L. Chandar, Arshad Momen, 22 pages in RevTeX format, available as gr-qc/9412019.

7. Quantum gravity and the algebra of tangles, by John Baez, Jour. Class. Quantum Grav. 10 (1993), 673 - 694.

8. On algebraic structures implicit in topological quantum field theories, by Louis Crane and David Yetter, 13 pages available as hep-th/9412025, figures available by request.

9. On the definition of 2-category of 2-knots, by V. M. Kharlamov and V. G. Turaev, preprint.

10. Non-involutory Hopf algebras and 3-manifold invariants, by Greg Kuperberg, preprint #19941128002, available from the AMS preprint server under subject 57 or 16 in the Mathematical Reviews Subject Classification Scheme.

11. If Hamilton had prevailed: quaternions in physics, by J. Lambek, McGill University preprint, Nov. 1994.

12. The life and times of Emmy Noether; contributions of E. Noether to particle physics, by Nina Byers, 32 pages in RevTeX format, available as hep-th/9411110.

    Reminiscences about many pitfalls and some successes of QFT within the last three decades, by B. Schroer, 52 pages, 'shar'-shell-archiv, consisting of 5 files, available as hep-th/9410085.

    My encounters - as a physicist - with mathematics, R. Jackiw, 13 pages, preprint available as hep-th/9410151.

13. Speedup in quantum computation is associated with attenuation of processing probability, by Karl Svozil, available as hep-th/9412046.

week47

A description of some new electronic venues for math and physics papers.

week48

1. Quantum groups from path integrals, by Daniel Freed, preprint, 41 pages in AMSTeX 2.1 format available as q-alg/9501025.

2. Higher algebraic structures and quantization, by Daniel Freed, Comm. Math. Phys. 159 (1994), 343-398; preprint available as hep-th/9212115.

3. Chern-Simons theory with finite gauge group, by Daniel Freed and Frank Quinn, Comm. Math. Phys. 156 (1993), 435-472.

4. Poisson structures on moduli of flat connections on Riemann surfaces and r-matrices, V. V. Fock and A. A. Rosly, preprint ITEP 72-92, June 1992, Moscow.

5. Combinatorial quantization of the Hamiltonian Chern-Simons theory, I & II, by Yu. Alekseev, H. Grosse, and V. Schomerus, hep-th/9403066 and hep-th/9408097.

6. Geometric quantization of Chern-Simons gauge theory, S. Axelrod, S. Della Pietra and E. Witten, Jour. Diff. Geom. 33 (1991), 787-902.

7. Metaplectic quantization of the moduli space of flat and parabolic bundles (after Peter Scheinhost), in Public. I. R. M. A. Strasbourg, 45 (1993), 43-70.

week49

1. Categories for the Working Mathematician, by S. Mac Lane, Springer, Berlin, 1988.

2. Higher-dimensional algebra and topological quantum field theory, by John Baez and James Dolan, Jour. Math. Phys. 36 (1995), 6073-6105. Available in Postscript form at tqft.ps - but without the crucial hand-drawn figures, alas.

3. Double construction for monoidal categories, by Christian Kassel and Vladimir Turaev, Publication de l'Institute de Recherche Mathematique Avancee, 1992.

4. Reconstruction in braided categories and a notion of commutative bialgebra, Martin Neuchl and Peter Schauenburg, Mathematisches Institut, Theresienstr. 39, 80333 Muenchen, Feb. 20, 1995.

5. Tannaka duality for arbitrary Hopf algebras, by Peter Schauenburg, Algebra-Berichte 66 (1992).

week50

1. Supersymmetric Yang-Mills theory on a four-manifold, by Edward Witten, Jour. Math. Phys. 35 (1994), 5101-5135.

2. Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases, by Louis Crane and Igor Frenkel, Jour. Math. Phys. 35 (1994), 5136-5154.

3. On the self-linking of knots, by Raoul Bott and Clifford Taubes, Jour. Math. Phys. 35 (1994), 5247-5287.

4. An explicit description of the symplectic struture of moduli spaces of flat connections, by Christopher King and Ambar Sengupta, Jour. Math. Phys. 35 (1994), 5338-5353.

   The semiclassical limit of the two-dimensional quantum Yang-Mills model, same authors, Jour. Math. Phys. 35 (1994), 5354-5363.

5. Topological interpretations of quantum Hall conductance, by D. J. Thouless, Jour. Math. Phys. 35 (1994), 5362-5372.

6. The noncommutative geometry of the quantum Hall effect, by J. Bellisard, A. van Elst, and H. Schulz-Baldes, Jour. Math. Phys. 35 (1994), 5373-5451.

7. Topology change in (2+1)-dimensional gravity, by Steve Carlip and R. Cosgrove, Jour. Math. Phys. 35 (1994), 5477-5493.

week51

1. Topological quantum field theory, by Edward Witten, Comm. Math. Phys. 117 (1988) 353.

2. Quantum field theory and the Jones polynomial, by Edward Witten, Comm. Math. Phys. 121 (1989) 351.

3. N = 2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant, by Matthias Blau and George Thompson, Comm. Math. Phys. 152 (1993), 41-71.

4. Knots and Physics, by Louis Kauffman, World Scientific Press, Singapore, 1991.

week52

1. Permutation City, by Greg Egan, published in Britain by Millenium (should be available in the U.S. by autumn).

2. Alberto Cattaneo, Teorie topologiche di tipo BF ed invarianti dei nodi, doctoral thesis, department of physics, University of Milan.

   Alberto Cattaneo, Paolo Cotta-Ramusino, Juerg Froehlich, and Maurizio Martellini, Topological BF theories in 3 and 4 dimensions, preprint available as hep-th/9505027.

week53

1. Ronald Brown, Out of line, Royal Institution Proceedings 64, 207-243.

2. A. J. Power, Why tricategories, preprint available as ECS-LFCS-94-289 from Laboratory for Foundations of Computer Science, University of Edinburgh.

3. P. Gabriel and F. Ulmer, Lokal praesentierbare Kategorien, in Springer Lecture Notes in Math 221 (1971).

   G. Kelly, Structures defined by finite limits in the enriched context I, Cahiers de Top. et. Geom. Diff. 23 (1982), 3-41.

   Michael Makkai and Robert Pare, Accessible categories: the foundations of categorical model theory, in Contemp. Math. 104 (1989).

week54

1. Timothy Porter, Abstract homotopy theory: the interaction of category theory and homotopy theory, lectures from the school on "Categories and Topology", Department of Mathematics, Universita di Genova, report #199, March 1992.

2. L. Loday, Spaces with finitely many non-trivial homotopy groups, Jour. Pure Appl. Algebra 24 (1982), 179-202.

3. Timothy Porter, Interpretations of Yetter's notion of G-coloring: simplicial fibre bundles and non-abelian cohomology, available electronically from his website, http://www.bangor.ac.uk/~mas013/preprint.html

4. David N. Yetter, Topological quantum field theories associated to finite groups and crossed G-sets, Journal of Knot Theory and its Ramifications 1 (1992), 1-20.

   TQFTs from homotopy 2-types, Journal of Knot Theory and its Ramifications 2 (1993), 113-123.

5. Justin Roberts, Skein theory and Turaev-Viro invariants, preprint. (Justin Roberts can be reached via email at J.D.Roberts@pmms.cam.ac.uk)

   Refined state-sum invariants of 3- and 4-manifolds, preprint.

   Skeins and mapping class groups, Math. Proc. Camb. Phil. Soc. 115 (1994), 53-77.

   G. Masbaum and Justin Roberts, On central extensions of mapping class groups, Mathematica Gottingensis, Schriftenreihe des Sonderforschungsbereichs Geometrie und Analysis, Heft 42 (1993).

6. Lawrence Breen, On the Classification of 2-Gerbes and 2-Stacks, Asterisque 225, 1994.

week55

1. Gary Au, The quest for quantum gravity, available as gr/qc-9506001.

2. Renate Loll, Nonperturbative solutions for lattice quantum gravity, preprint available as gr-qc/9502006.

3. C. Rovelli and L. Smolin, Spin networks in quantum gravity, preprint available as gr/qc-9505006.

4. J. Baez, Spin networks in nonperturbative quantum gravity, preprint available as gr-qc/9504036, or at net.tex.

5. Abhay Ashtekar, Jerzy Lewandowski, Don Marolf, Jose Mourao, and Thomas Thiemann, Quantization of diffeomorphism invariant theories of connections with local degrees of freedom, to appear in the November 1995 Jour. Math. Phys. special issue on diffeomorphism-invariant field theory, preprint available as gr-qc/9504018.

6. Steve Sawin, Path integration in two-dimensional topological quantum field theory, to appear in the November 1995 Jour. Math. Phys. issue on diffeomorphism-invariant field theory, preprint available as gr/qc-9505040.

week56

1. Lee Smolin, Linking topological quantum field theory and nonperturbative quantum gravity, available as gr-qc/9505028.

2. H. Kodama, Holomorphic wavefunction of the universe, Phys. Rev. D42 (1990), 2548-2565.

3. Louis Crane: Clock and category: is quantum gravity algebraic?, to appear in the November 1995 special issue of Jour. Math. Phys. on diffeomorphism-invariant physics, preprint available as gr-qc/9504038.

4. John Baez, Quantum gravity and the algebra of tangles, Jour. Class. Quant. Grav. 10 (1993), 673-694, also available (without the all-important pictures!) as tang.tex.

week57

1. Lee Smolin, Linking topological quantum field theory and nonperturbative quantum gravity, available as gr-qc/9505028.

2. G 't Hooft, Dimensional reduction in quantum gravity, preprint available as gr-qc/9310006.

3. L. Susskind, The world as a hologram, to appear in the November 1995 special issue of Jour. Math. Phys. on diffeomorphism-invariant physics, preprint available as hep-th/9409089.

   L. Susskind, Strings, black holes and Lorentz contractions, preprint available as hep-th/9308139.

week58

1. John Barrett, Quantum gravity as topological quantum field theory, to appear in the November 1995 special issue of Jour. Math. Physics, preprint available as gr-qc/9506070.

2. M. Kapranov and V. Voevodsky, 2-Categories and Zamolodchikov tetrahedra equations, in Proc. Symp. Pure Math. 56, Part 2 (1994), AMS, Providence, pp. 177-260.

3. David Yetter, Categorical linear algebra: a setting for questions from physics and low-dimensional topology, Kansas U. preprint.

4. Eugenia Cesar de Sa, Automorphisms of 3-manifolds and representations of 4-manifolds, Ph.D. thesis, University of Warwick, 1977.

5. John Baez, 4-dimensional BF theory as a topological quantum field theory, preprint available as q-alg/9507006. Also available as bf.tex, with a figure in Postscript form, figure.ps.

6. Timothy Porter, TQFTs from homotopy n-types, University of Wales, available electronically from his website, http://www.bangor.ac.uk/~mas013/preprint.html

7. David Yetter, TQFTs from homotopy 2-types, Journal of Knot Theory and its Ramifications 2 (1993), 113-123.

week59

1. Geoffrey M. Dixon, Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics, Kluwer Press, ISBN 0-7923-2880-6.

2. William Fulton and Joe Harris, Representation Theory --- a First Course, Springer Verlag, Berlin, 1991.

3. Geoffrey Dixon, Octonion X-product orbits, preprint available as hep-th/9410202.

   Octonion X-product and E8 lattices, preprint available as hep-th/9411063.

   Octonions: E8 lattice to Lambda_{16}, preprint available as hep-th/9501007.

   Octonions: invariant representation of the Leech lattice, preprint available as hep-th/9504040.

   Octonions: invariant Leech lattice exposed, preprint available as hep-th/9506080.

week60

1. N. P. Landsman, Rieffel induction as generalized quantum Marsden-Weinstein reduction, Journal of Geometry and Physics 15 (1995), 285-319.

2. T. Ohtsuki, Finite type invariants of integral homology 3-spheres, preprint, 1994.

   L. Rozansky, The trivial connection contribution to Witten's invariant and finite type invariants of rational homology spheres, preprint available as q-alg/9505015.

   Stavros Garoufalidis, On finite type 3-manifold invariants I, MIT preprint, 1995.

   Stavros Garoufalidis and Jerome Levine, On finite type 3-manifold invariants II, MIT preprint, June 1995. (Garoufalidis is at stavros@math.mit.edu, and Levine is at levine@max.math.brandeis.edu.)

   Ruth J. Lawrence, Asymptotic expansions of Witten-Reshetikhin-Turaev invariants for some simple 3-manifolds, to appear in Jour. Math. Physics.

3. Thomas Friedrich, Neue Invarianten der 4-dimensionalen Mannigfaltigkeiten, Berlin preprint.

4. Andre Joyal, Ross Street, and Dominic Verity, Traced monoidal categories, to appear in Math. Proc. Camb. Phil. Soc..

5. Michael Reisenberger, Worldsheet formulations of gauge theories and gravity, University of Utrecht preprint, 1994, available as gr-qc/9412035.

6. John Baez and Stephen Sawin, Functional integration on spaces of connections, available as q-alg/9507023.

7. John Baez, Javier P. Muniain and Dardo Piriz, Quantum gravity hamiltonian for manifolds with boundary, available as gr-qc/9501016.

week61

1. Alex J. Feingold, Igor B. Frenkel, and John F. X. Rees, Spinor construction of vertex operator algebras, triality, and E₈⁽¹⁾, Contemp. Math. 121, AMS, Providence Rhode Island. ISBN 0-8218-5128-4.

2. Claude Chevalley, The algebraic theory of spinors, Columbia U. Press, New York, 1954.

3. Ian R. Porteous, Topological Geometry, Cambridge U. Press, Cambridge, 1981.

4. R. D. Schafer, An Introduction to Non-Associative Algebras, Dover, New York, 1995.

5. I. L. Kantor and A. S. Solodovnikov, Hypercomplex Numbers -- an Elementary Introduction to Algebras, Springer-Verlag, Berlin, 1989, ISBN 0-387-96980-2 (acid-free paper); ISBN 3-540-96980-2; translation of "Giperkompleksnye chisla", Moscow, 1973.

week62

1. Victor Guillemin and Shlomo Sternberg, Variations on a Theme by Kepler, American Mathematical Society, Providence, Rhode Island, 1990.

2. Problems of Present Day Mathematics in Mathematical Developments Arising from Hilbert's Problems, ed. F. E. Browder, Proc. Symp. Pure Math. 28, American Mathematical Society, Providence, Rhode Island, 1976.

3. M. Hazewinkel, W. Hesselink, D. Siermsa, and F. D. Veldkamp, The ubiquity of Coxeter-Dynkin diagrams (an introduction to the ADE problem), Niew. Arch. Wisk., 25 (1977), 257-307.

week63

1. Hermann Weyl, Symmetry, Princeton University Press, Princeton, New Jersey, 1989.

2. John Frank Adams, Lectures on Lie groups, Benjamin, New York, 1969.

week64

1. Juergen Fuchs, Affine Lie Algebras and Quantum Groups, Cambridge Monographs on Mathematical Physics, Cambridge U. Press, Cambridge 1992, ISBN 0-521-41593-4.

2. Victor Kac, Infinite Dimensional Lie Algebras, 3rd ed., Cambridge University Press, Cambridge, 1990.

3. Loop groups, by Andrew Pressley and Graeme Segal, Oxford University Press, Oxford, 1986.

week65

1. John H. Conway and Neil J. A. Sloane, Sphere Packings, Lattices and Groups, second edition, Grundlehren der mathematischen Wissenschaften 290, Springer-Verlag, 1993.

2. Geoffrey Dixon, Octonion X-product and E8 lattices, preprint available as hep-th/9411063.

3. John McKay, Graphs, singularities and finite groups, in Proc. Symp. Pure Math. vol 37, Amer. Math. Soc. (1980), pages 183- and 265-.

   John McKay, Representations and Coxeter Graphs, in "The Geometric Vein" Coxeter Festschrift (1982), Springer-Verlag, Berlin, pages 549-.

   John McKay, A rapid introduction to ADE theory, http://math.ucr.edu/home/baez/ADE.html

4. Pavel Etinghof and Michael Khovanov, Representations of tensor categories and Dynkin diagrams, preprint available as hep-th/9408078.

5. Jurg Froehlich and Thomas Kerler, Quantum Groups, Quantum Categories, and Quantum Field Theory, Springer Lecture Notes in Mathematics 1542, Springer-Verlag, Berlin, 1991.

6. M. Hazewinkel, W. Hesselink, D. Siermsa, and F. D. Veldkamp, The ubiquity of Coxeter-Dynkin diagrams (an introduction to the ADE problem), Niew. Arch. Wisk., 25 (1977), 257-307.

7. Capelli and Zuber, Comm. Math. Phys. 113 (1987) 1.

8. Kato, Mod. Phys. Lett. A2 (1987) 585.

9. Claude Itzykson and Jean-Michel Drouffe, Statistical Field Theory, 1: From Brownian Motion to Renormalization and Lattice Gauge Theory, and 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems. Cambridge U. Press, 1989.

week66

1. The ten billionth hexadecimal digit of pi is 9, by Simon Plouffe, http://groups.google.com/groups?selm=451p8p%24qcr%40morgoth.sfu.ca&output;=gplain

2. David Bailey, Peter Borwein and Simon Plouffe, On the rapid computation of various polylogarithmic constants, available in postscript form from http://www.cecm.sfu.ca/personal/pborwein/PISTUFF/Apistuff.html

3. The miraculous Bailey-Borwein-Plouffe pi algorithm, by Steven Finch, http://www.lacim.uqam.ca/~plouffe/Simon/Miraculous.pdf

4. Ron Solomon, On finite simple groups and their classification, AMS Notices Vol. 45, February 1995, 231-239.

5. Igor Frenkel, James Lepowsky, and Arne Meurman, Vertex Operator Algebras and the Monster, Academic Press, Boston, 1988.

6. Friedrich Hirzebruch, Thomas Berger, and Rainer Jung, Manifolds and Modular Forms, translated by Peter S. Landweber, pub. Braunschweig, Vieweg, 1992.

7. Richard E. Borcherds, The Monster Lie-algebra, Adv. Math. 83 (1990), 30-47.

   Richard E. Borcherds, Monstrous Moonshine and monstrous Lie-superalgebras, Invent. Math. 109 (1992), 405-444.

week67

1. Margaret Wertheim, Pythagoras' Trousers: God, Physics, and the Gender Wars, Times Books/Random House, New York, 1995.

2. Stephen W. Hawking, Virtual black holes, preprint available as hep-th/9510029.

3. Kerson Huang, Quarks, Leptons, and Gauge Fields, World Scientific Publishing Co., Singapore, 1982. ISBN 9971-950-03-0.

4. Ted Jacobson, Thermodynamics of spacetime: the Einstein equation of state, preprint available as gr-qc/9504004.

5. Lee Smolin, The Bekenstein bound, topological quantum field theory and pluralistic quantum field theory, preprint available as gr-qc/9508064.

6. Rodolfo Gambini, Octavio Obregon and Jorge Pullin, Towards a loop representation for quantum canonical supergravity, preprint available as hep-th/9508036.

7. Roh Suan Tung and Ted Jacobson, Spinor one-forms as gravitational potentials, preprint available as gr-qc/9502037.

8. Joseph Polchinski and Edward Witten, Evidence for Heterotic - Type I String Duality, preprint available as hep-th/9510169.

week68

1. Robert Goldblatt, Topoi, the Categorial Analysis of Logic, Studies in logic and the foundations of mathematics vol. 98, North-Holland, New York, 1984.

2. Saunders Mac Lane and Ieke Moerdijk, Sheaves in Geometry and Logic: A First Introduction to Topos Theory, Springer-Verlag, New York, 1992.

3. Michael Barr and Charles Wells, Toposes, Triples and Theories, Springer-Verlag, New York, 1983. Available for free electronically at http://www.cwru.edu/artsci/math/wells/pub/ttt.html

4. Frank Close, Are glueballs and hybrids found?, available as hep-ph/9509245. To appear in Proceedings of Hadron95.

   J. Sexton, A. Vaccarino, D. Weingarten, Numerical evidence for the observation of a scalar glueball, available as hep-lat/9510022.

5. R. Plaga, Proposal for an experimental test of the many-worlds interpretation of quantum mechanics, preprint available as quant-ph/9510007

6. Nicholas Landsman, Against the Wheeler-DeWitt equation, preprint available as gr-qc/9510033.

7. Pavel Etingof and David Kazhdan, Quantization of Lie bialgebras, I, preprint available in AMSTeX form as q-alg/9506005.

   Quantization of Poisson algebraic groups and Poisson homogeneous spaces, preprint available in AMSTeX form as q-alg/9510020.

8. Steve Carlip, Statistical mechanics and black hole entropy, preprint available as gr-qc/9509024.

   Claudio Teitelboim, Statistical thermodynamics of a black hole in terms of surface fields, preprint available as hep-th/9510180.

9. Jorge Griego, Is the third coefficient of the Jones knot polynomial a quantum state of gravity?, preprint available as gr-qc/9510051.

   The Kauffman bracket and the Jones polynomial in quantum gravity, preprint available as gr-qc/9510050.

week69

1. Marcia Bartusiak, When the universe began, what time was it?, Technology Review (edited at the Massachusetts Institute of Technology), November/December 1995, pp. 54-63.

2. C. J. Isham, Structural issues in quantum gravity, plenary session lecture given at the GR14 conference, Florence, August 1995, preprint available as gr-qc/9510063.

3. Abhay Ashtekar, Polymer geometry at Planck scale and quantum Einstein equations.

4. Renate Loll, Spectrum of the volume operator in quantum gravity, 14 pages in plain tex, with 4 figures (postscript, compressed and uu-encoded), available as gr-qc/9511030.

week70

1. Basic Research Institute in the Mathematical Sciences, New Connections web page, http://www-uk.hpl.hp.com/brims/

2. A. C. Elitzur and L. Vaidman, Quantum mechanical interaction-free measurements, Foundations of Phys. 23 (1993), 987-997.

   Richard Josza, Counterfactual quantum computation. (Josza's email address is p08205@prime-a.plymouth.ac.uk)

3. Eric Goubault, Schedulers as abstract interpretations of HDA, in Proc. of PEPM '95, ACM Press, 1995.

   Higher-dimensional automata, part I. Technical report, Ecole Normale Superieure, to appear 1995.

4. Vaughan Pratt, Time and information in sequential and concurrent computation, Proc. Theory and Practice of Parallel Programming, Sendai, Japan, 1994.

5. Craig C. Squier, Word problems and a homological finiteness condition for monoids, Jour. Pure Appl. Algebra 49 (1987), 201-217.

   Craig C. Squier, A finiteness condition for rewriting systems, revision by F. Otto and Y. Kobayashi, to appear in Theoretical Computer Science.

   Craig C. Squier and F. Otto, The word problem for finitely presented monoids and finite canonical rewriting systems, in J. P. Jouannuad (ed.), Rewriting Techniques and Applications, Lecture Notes in Computer Science 256 (1987), 74-82.

6. Yves Lafont and Alain Proute, Church-Rosser property and homology of monoids, to appear in Mathematical Structures in Computer Science.

   Yves Lafont, A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier), CNRS preprint. (Lafont's email address is lafont@lmd.univ-mrs.fr)

week71

1. John Baez and James Dolan, n-Categories, sketch of a definition, http://math.ucr.edu/home/baez/ncat.def.html

2. Erik Verlinde, Global aspects of electric-magnetic duality, Nuc. Phys. B455 (1995), 211-225, preprint available as hep-th/9506011.

   George Thompson, New results in topological field theory and abelian gauge theory, 64 pages, preprint available as hep-th/9511038.

3. Thomas Thiemann, An account of transforms on (A/G)^bar, preprint available as gr-qc/9511049.

   Thomas Thiemann, Reality conditions inducing transforms for quantum gauge field theory and quantum gravity, preprint available as gr-qc/9511057.

   Abhay Ashtekar, A generalized Wick transform for gravity, preprint available as gr-qc/9511083.

   Renate Loll, Making quantum gravity calculable, preprint available as gr-qc/9511080.

   Rodolfo Gambini and Jorge Pullin, A rigorous solution of the quantum Einstein equations, preprint avilable in RevTex form as gr-qc/9511042, four figures included with epsf.

4. Matt Greenwood and Xiao-Song Lin, On Vassiliev knot invariants induced from finite type, 14 pages in AMSLaTeX format available as q-alg/9506001, with 9 figures not included. The compressed archive of the amslatex file and 9 postscript figure files can be obtained at ftp://math.columbia.edu/pub/lin/gl.tar.Z

   Lev Rozansky, On finite type invariants of links and rational homology spheres derived from the Jones polynomial and Witten- Reshetikhin-Turaev invariant, preprint available as q-alg/9511025.

   Scott Axelrod, Overview and warmup example for perturbation theory with instantons, preprint available as hep-th/9511196.

5. Alan Carey, Jouko Mickelsson, and Michael Murray, Index theory, gerbes, and Hamiltonian quantization, 16 pages in Plain TeX (inputting AMSTeX), preprint available as hep-th/9511151.

   Alan Carey, M. K. Murray and B. L. Wang, Higher bundle gerbes and cohomology classes in gauge theories, preprint available as hep-th/9511169

6. Jean-Luc Brylinski, Holomorphic gerbes and the Beilinson regulator, in Proc. Int. Conf. on K-Theory (Strasbourg, 1992), to appear in Asterisque.

   Jean-Luc Brylinski and D. A. McLaughlin, The geometry of degree-four characteristic classes and of line bundles on loop spaces I, Duke Math. Jour. 75 (1994), 603-638.

   Jean-Luc Brylinski and D. A. McLaughlin, Cech cocyles for characteristic classes.

7. Joe Polchinski, Recent results in string duality, preprint available as hep-th/9511157, uses PTPTeX.sty.

8. Leonard Susskind and John Uglum, String physics and black holes, preprint available as hep-th/9511227, needs espcrc2.sty.

9. Boguslaw Broda, A gauge-field approach to 3- and 4-manifold invariants, preprint available in TeX form as q-alg/9511010.

10. John Baez and Martin Neuchl, Higher-Dimensional Algebra I: Braided Monoidal 2-Categories, 51 pages, available as a compressed PostScript file at http://math.ucr.edu/home/baez/bm2cat.ps.Z

    This paper is q-alg/9511013, but looking for it there will just lead you to the above site.

week72

1. Kelly Jay Davis, M-Theory and String-String Duality, 28 pages, preprint available as hep-th/9601102, uses harvmac.tex.

2. Edward Witten, Five-branes and M-Theory On An Orbifold, preprint available as hep-th/9512219.

3. Abhay Ashtekar, Polymer geometry at Planck scale and quantum Einstein equations, preprint available as hep-th/9601054.

   Roumen Borissov, Seth Major and Lee Smolin, The geometry of quantum spin networks, preprint available as gr-qc/9512043, 35 Postscript figures, uses epsfig.sty.

   Bernd Bruegmann, On the constraint algebra of quantum gravity in the loop representation, preprint available as gr-qc/9512036.

   Kiyoshi Ezawa, Nonperturbative solutions for canonical quantum gravity: an overview, preprint available as gr-qc/9601050

   Kiyoshi Ezawa, A semiclassical interpretation of the topological solutions for canonical quantum gravity, preprint available as gr-qc/9512017.

   Jorge Griego, Extended knots and the space of states of quantum gravity, preprint available as gr-qc/9601007.

   Seth Major and Lee Smolin, Quantum deformation of quantum gravity, preprint available as gr-qc/9512020.

4. Thomas Kerler, Genealogy of nonperturbative quantum-invariants of 3-manifolds: the surgical family, preprint available as q-alg/9601021.

week73

1. Biological Asymmetry and Handedness, Ciba Foundation Symposium 162, John Wiley and Sons, 1991.

   D. K. Kondepudi and D. K. Nelson, Weak neutral currents and the origins of molecular chirality, Nature 314, pp. 438-441.

week74

1. John Baez et al, General relativity tutorial, http://math.ucr.edu/home/baez/gr/gr.html

2. Abhay Ashtekar and Jerzy Lewandowski, Quantum Theory of Geometry I: Area Operators, 31 pages, to appear in Classical and Quantum Gravity, preprint available as gr-qc/9602046.

   Jerzy Lewandowski, Volume and Quantizations, preprint available as gr-qc/9602035.

   Roberto De Pietri and Carlo Rovelli, Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity, 38 pages, 5 Postscript figures, uses RevTeX 3.0 and epsfig.sty, preprint available as gr-qc/9602023.

3. Alan Weinstein, Groupoids: unifying internal and external symmetry, available as http://math.berkeley.edu/~alanw/Groupoids.ps

week75

1. J. P. May, Simplicial Objects in Algebraic Topology, Van Nostrand, Princeton, 1968.

week76

1. Relativistic Heavy Ion Collider homepage, http://www.rhic.bnl.gov/~rhicb/rhic_home/RHIC.html

   Phase diagram of nuclear matter and nuclear collisions, http://www.rhic.bnl.gov/~rhicb/GIF/9508pdg.gif

2. Adriano Di Giacomo, Mechanisms of colour confinement, preprint available as hep-th/9603029.

week77

1. Center for Gravitational Physics and Geometry (CGPG) home page, http://vishnu.nirvana.phys.psu.edu/

   Reading list on the new variables: http://vishnu.nirvana.phys.psu.edu/readinglist/readinglist.html

2. Rodolfo Gambini and Jorge Pullin, The general solution of the quantum Einstein equations?, preprint in Revtex format, 7 figures included with psfig, available as gr-qc/9603019.

week78

1. Higher algebraic structures and quantization, by Daniel Freed, Commun. Math. Phys. 159 (1994), 343-398, also available as hep-th/9212115.

week79

1. Bertram Kostant, The graph of the truncated icosahedron and the last letter of Galois, Notices of the AMS, 959-968 (42), September 1995. Also available as http://www.ams.org/publications/notices/199509/kostant.html

2. John Baez, Some thoughts on the number 6, http://math.ucr.edu/home/baez/six.html

3. P. W. Fowler and D. E. Manolpoulos, An Atlas of Fullerenes, Oxford University Press, 1995.

   M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund, Science of Fullerenes and Carbon Nanotubules, Academic Press, New York, 1994.

   G. Chung, B. Kostant and S. Sternberg, Groups and the buckyball, in Lie Theory and Geometry, eds. J.-L. Brylinski, R. Brylinski, V. Guillemin and V. Kac, Birkhauser, 1994.

4. Southern Chemical Group homepage, http://www.southchem.com/index.html

week80

1. Huw Price, Time's Arrow and Archimedes' Point: New Directions for a Physics of Time, Oxford University Press, 1996.

2. Stephen Hawking and Roger Penrose, The Nature of Space and Time, Princeton University Press, 1996.

3. Charles Misner, Kip Thorne and John Wheeler, Gravitation, Freeman Press, 1973.

4. Ignazio Ciufolini and John Archibald Wheeler, Gravitation and Inertia, Princeton University Press, 1995.

5. Kip Thorne, Richard Price and Douglas Macdonald, eds., Black Holes: The Membrane Paradigm, 1986.

6. Gravity Probe B, http://www-leland.stanford.edu/~michman/RELATIVITYmosaic/GPBmosaic/GPB.html

7. LIGO project home page, http://www.ligo.caltech.edu/

8. Ross Street, Categorical structures, in Handbook of Algebra, vol. 1, ed. M. Hazewinkel, Elsevier, 1996.

9. G. Maxwell Kelly and Ross Street, Review of the elements of 2-categories, Springer Lecture Notes in Mathematics 420, Berlin, 1974, pp. 75-103.

week81

1. D. J. Bird et al, Detection of a cosmic ray with measured energy well beyond the expected spectral cutoff due to cosmic microwave radiation, preprint available as astro-ph/9410067

   P. Bhattacharjee and G. Sigl, Monopole annihilation and highest energy cosmic rays, preprint available as astro-ph/9412053.

   R. J. Protheroe and P. A. Johnson, Are topological defects responsible for the 300 EeV cosmic rays?, preprint available as astro-ph/9605006.

2. Jean-Luc Brylinski and Dennis A. McLaughlin, The geometry of degree four characteristic classes and of line bundles on loop spaces II, preprint.

   Jean-Luc Brylinski, Central extensions and reciprocity laws, preprint.

   Jean-Luc Brylinski, Coadjoint orbits of central extensions of gauge groups, preprint.

   Jean-Luc Brylinski and Dennis A. McLaughlin, The geometry of two dimensional symbols, preprint.

week82

1. Advances in Applied Clifford Algebras, ed. Jaime Keller. (Subscriptions are available from Mrs. Irma Aragon, F. Q., UNAM, Apartado 70-528, 04510 Mexico, D.F., MEXICO, for US $10 per year.)

2. H. Blaine Lawson, Jr. and Marie-Louise Michelson, "Spin Geometry", Princeton U. Press, Princeton, 1989.

3. Dale Husemoller, "Fibre Bundles", Springer-Verlag, Berlin, 1994.

4. Ralph L. Cohen, John D. S. Jones, and Graeme B. Segal, Morse theory and classifying spaces, preprint as of Sept. 13, 1991.

5. Graeme B. Segal, Classifying spaces and spectral sequences, Pub. IHES 34 (1968), 105-112.

6. Ross Street, Descent theory, preprint of talks given at Oberwolfach, Sept. 17-23, 1995.

   Ross Street, Fusion operators and cocycloids in monoidal categories, preprints.

7. Viqar Husain, Intersecting-loop solutions of the hamiltonian constraint of quantum general relativity, Nucl. Phys. B313 (1989), 711-724.

   Viqar Husain and Karel V. Kuchar, General covariance, new variables, and dynamics without dynamics, Phys. Rev. D 42 (1990), 4070-4077.

   Viqar Husain, Einstein's equations and the chiral model, to appear in Phys. Rev. D, preprint available as gr-qc/9602050.

8. The Interface of Knots and Physics, ed. Louis H. Kauffman, Proc. Symp. Appl. Math. 51, American Mathematical Society, Providence, Rhode Island, 1996. Contains:

   Louis H. Kauffman, Knots and statistical mechanics

   Ruth J. Lawrence, An introduction to topological field theory

   Dror Bar-Natan, Vassiliev and quantum invariants of braids

   Samuel J. Lomonaco, The modern legacies of Thomson's atomic vortex theory in classical electrodynamics

   John C. Baez, Spin networks in nonperturbative quantum gravity

week83

1. Alain Connes, Gravity coupled with matter and the foundation of non-commutative geometry, preprint available as hep-th/9603053.

   Ali H. Chamseddine and Alain Connes, The spectral action principle, preprint available as hep-th/9606001.

2. Francis Borceux, Handbook of Categorical Algebra, Cambridge U. Press 1994. Volume 1: Basic Category Theory. Volume 2: Categories and Structure. Volume 3: Categories of Sheaves.

week84

1. AltaVista, http://www.altavista.digital.com/

2. CYC project homepage, http://www.cyc.com/

3. Douglas B. Lenat and R.V. Guha, Building Large Knowledge-Based Systems: Representation and Inference in the Cyc Project, Addison-Wesley, Reading, Mass., 1990.

4. Vaughan Pratt, CYC Report, http://boole.stanford.edu/pub/cyc.report

5. Project Xanadu, http://xanadu.net/the.project

6. Ted Kaehler's backlinks browser, http://www.foresight.org/backlinks1.3.1.html

7. Backlinking news at the Foresight Institute, http://www.foresight.org/backlinks.news.html

   Robin Hanson's ideas on backlinking, http://www.hss.caltech.edu/~hanson/findcritics.html

8. Francesco Fucito, Maurizio Martellini and Mauro Zeni, The BF formalism for QCD and quark confinement, preprint available as hep-th/9605018.

9. Ioannis Tsohantjis, Alex C. Kalloniatis, and Peter D. Jarvis, Chord diagrams and BPHZ subtractions, preprint available as hep-th/9604191.

10. Masaki Kashiwara and Yoshihisa Saito, Geometric construction of crystal bases, q-alg/9606009.

week85

1. Troy Schilling, Non-covariance of the generalized holonomies: Examples, preprint available as gr-qc/9503064.

2. Thomas Thiemann, Quantum Spin Dynamics (QSD), preprint available as gr-qc/9606089.

   Thomas Thiemann, Quantum Spin Dynamics (QSD) II, preprint available as gr-qc/9606090.

   Thomas Thiemann, Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity, to appear in Physics Letters B, preprint available as gr-qc/9606088.

   Thomas Thiemann, Closed formula for the matrix elements of the volume operator in canonical quantum gravity, preprint available as gr-qc/9606091.

   Thomas Thiemann, A length operator for canonical quantum gravity, preprint available as gr-qc/9606092.

3. Kirill Krasnov, Quantum loop representation for fermions coupled to Einstein-Maxwell field, Phys. Rev. D53 (1996), 1874; preprint available as gr-qc/9506029.

4. Carlo Rovelli and Hugo Morales-Tecotl, Fermions in quantum gravity, Phys. Rev. Lett. 72 (1994), 3642-3645.

   Carlo Rovelli and Hugo Morales-Tecotl, Nucl. Phys. B451 (1995), 325, preprint available as gr-qc/9401011.

week86

1. Discreteness of area and volume in quantum gravity, by Carlo Rovelli and Lee Smolin, 36 pages, available as gr-qc/9411005.

   Abhay Ashtekar and Jerzy Lewandowski, Quantum theory of geometry I: area operators, 31 pages, to appear in the Classical and Quantum Gravity special issue dedicated to Andrzej Trautman, preprint available as gr-qc/9602046.

2. Junichi Iwasaki, A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces, University of Pittsburgh, preprint available as gr-qc/9410010.

3. Michael Reisenberger, Worldsheet formulations of gauge theories and Gravity, University of Utrecht preprint, 1994, available as gr-qc/9412035.

4. Renate Loll, The volume operator in discretized quantum gravity, preprint available as gr-qc/9506014, 15 pages.

   Renate Loll, Spectrum of the volume operator in quantum gravity, preprint available as gr-qc/9511030, 14 pages.

5. Jerzy Lewandowski, Volume and quantizations, preprint available as gr-qc/9602035, 8 pages.

   Abhay Ashtekar and Jerzy Lewandowski, Quantum theory of geometry II: volume operators, manuscript in preparation.

week87

1. G. Scharf, Finite quantum electrodynamics: the causal approach, Springer-Verlag, Berlin, 1995.

2. J. F. Colombeau, "Multiplication of Distributions: a Tool in Mathematics, Numerical Engineering, and Theoretical Physics," Lecture Notes in Mathematics 1532, Springer, Berlin, 1992.

3. Carlo Rovelli, Loop quantum gravity and black hole physics, preprint available as gr-qc/9608032.

   Kirill Krasnov, The Bekenstein bound and non-perturbative quantum gravity, preprint available as gr-qc/9603025.

   Kirill Krasnov, On statistical mechanics of gravitational systems, preprint available as gr-qc/9605047.

4. Gary Horowitz, The origin of black hole entropy in string theory, preprint available as gr-qc/9604051.

   Gary T. Horowitz and Donald Marolf, Counting states of black strings with traveling waves, preprint available as hep-th/9605224.

   Gary T. Horowitz and Donald Marolf, Counting states of black strings with traveling waves II, preprint available as hep-th/9606113.

5. Hugo Fort, Rodolfo Gambini and Jorge Pullin, Lattice knot theory and quantum gravity in the loop representation, preprint available as gr-qc/9608033.

week88

1. John Baez, The Hamiltonian constraint in the loop representation of quantum gravity, preprint available in LaTeX form at http://math.ucr.edu/home/baez/hamiltonian/. A less technical version of this appears in Jorge Pullin's newsletter Matters of Gravity, issue 8, at http://www.phys.lsu.edu//mog/mog8/node7.html.

2. Ted Jacobson, 1+1 sector of 3+1 gravity, Class. Quant. Grav. 13 (1996), L1-L6.

   Peter Schaller and Thomas Strobl, A brief introduction to Poisson sigma-models, preprint available as hep-th/9507020.

   Peter Schaller and Thomas Strobl, Poisson sigma-models: a generalization of 2d gravity-Yang-Mills systems, preprint available as hep-th/9411163.

week89

1. Jorge Pullin, ed., Matters of Gravity, first 8 issues now available at http://www.phys.lsu.edu//mog, or latest issue at gr-qc/9609008.

2. MacCallum's gravity mailing list: to subscribe send polite email to M.A.H.MacCallum@qmw.ac.uk

3. Erwin Schroedinger Institute preprint archive, available at http://www.esi.ac.at/ESI-Preprints.html. Recent preprints include:

   Abhay Ashtekar and Alejandro Corichi, Photon inner-product and the Gauss linking number.

   Abhay Ashtekar, Donald Marolf, Jose Mourao and Thomas Thiemann, SU(N) quantum Yang-Mills theory in 2 dimensions: a complete solution.

   Hugo Fort, Rodolfo Gambini and Jorge Pullin, Lattice knot theory and quantum gravity in the loop representation, also available as gr-qc/9608033.

   Michael Reisenberger, A left-handed simplicial action for Euclidean GR.

   Carlo Rovelli, Loop quantum gravity and black hole physics.

4. Jerzy Lewandowski and Jacek Wilsniewski, 2+1 sector of 3+1 gravity, preprint available as gr-qc/9609019.

5. Lee Smolin, The classical limit and the form of the Hamiltonian constraint in nonperturbative quantum gravity, preprint available as gr-qc/9609034.

6. Lee Smolin, Three dimensional strings as collective coordinates of four dimensional quantum gravity, preprint available as gr-qc/9609031.

7. Michael Dine, String theory dualities, preprint available as hep-th/9609051.

8. John Baez and Martin Neuchl, Higher-dimensional algebra I: braided monoidal 2-categories, 51 pages, available as a compressed PostScript file at http://math.ucr.edu/home/baez/bm2cat.ps.Z.

9. Categories for the Working Mathematician, by Saunders Mac Lane, Springer, Berlin, 1988.

10. Ross Street, Categorical structures, in Handbook of Algebra, vol. 1, ed. M. Hazewinkel, Elsevier, 1996.

week90

1. Claude C. Chevalley, The algebraic theory of spinors, Columbia University Press, New York, 1954.

2. F. Reese Harvey, Spinors and Calibrations, Academic Press, Boston, 1990.

3. Ian R. Porteous, Topological geometry, 2nd ed., Cambridge University Press, Cambridge, 1981.

4. Ian R. Porteous, Clifford algebras and the classical groups, Cambridge University Press, Cambridge, 1995.

5. Hans Freudenthal and H. de Vries, Linear Lie groups, Academic Press, New York, 1969.

6. Alex J. Feingold, Igor B. Frenkel, and John F. X. Rees, Spinor construction of vertex operator algebras, triality, and E_8^{(1)}, Contemp. Math. 121, AMS, Providence Rhode Island, ISBN 0-8218-5128-4.

week91

1. John H. Conway and Neil J. A. Sloane, Sphere Packings, Lattices and Groups, second edition, Grundlehren der mathematischen Wissenschaften 290, Springer-Verlag, 1993.

2. Frank D. (Tony) Smith, Sets and C^n; quivers and A-D-E; triality; generalized supersymmetry; and D4-D5-E6, preprint available as hep-th/9306011.

3. Tony Smith's home page, http://www.innerx.net/personal/tsmith/TShome.html

4. Hans Freudenthal, Adv. Math. 1 (1964) 143.

5. Jacques Tits, Indag. Math. 28 (1966) 223-237.

6. Kevin McCrimmon, Jordan Algebras and their Applications, Bull. AMS 84 (1978) 612-627, at pp. 620-621

7. Tony Smith, Freudenthal-Tits magic square, http://www.innerx.net/personal/tsmith/FTsquare.html

week92

1. Applications of negative dimensional tensors, by Roger Penrose, in Combinatorial Mathematics and its Applications, ed. D. J. A. Welsh, Academic Press, 1971.

2. Sidney Coleman, Aspects of Symmetry, Cambridge University Press, 1989. ISBN 0 521 26706 4 (hardback) and ISBN 0 521 31827 0 (paperback).

3. Dror Bar-Natan, Lie algebras and the four color theorem, preprint available as q-alg/9606016.

4. Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas, A new proof of the four-colour theorem, Electronic Research Announcements of the American Mathematical Society 2 (1996), 17-25. Available at http://www.ams.org/journals/era/1996-02-01/

week93

1. Paul Langacker, Implications of neutrino mass, http://dept.physics.upenn.edu/neutrino/jhu/jhu.html

2. John Baez, Spin, statistics, CPT and all that jazz, http://math.ucr.edu/home/baez/spin.stat.html

3. John H. Schwarz, Introduction to supersymmetry, in Superstrings and Supergravity, Proc. of the 28th Scottish Universities Summer School in Physics, ed. A. T. Davies and D. G. Sutherland, University Printing House, Oxford, 1985.

4. John H. Schwarz, Introduction to superstrings, in Superstrings and Supergravity, Proc. of the 28th Scottish Universities Summer School in Physics, ed. A. T. Davies and D. G. Sutherland, University Printing House, Oxford, 1985.

week94

1. Frank Wilczek, Asymptotic freedom, preprint available as hep-th/9609099.

2. N. K. Nielsen, Am. J. Phys. 49, 1171 (1981).

3. R. J. Hughes, Nucl. Phys. B186, 376 (1981).

4. Richard Feynman, Robert Leighton, and Matthew Sands, "The Feynman Lectures on Physics", Addison-Wesley, Reading, Mass., 1964.

5. Barry Simon, "Functional Integration and Quantum Physics ", Academic Press, 1979.

week95

1. Laurie M. Brown, ed., "Renormalization: From Lorentz to Landau (and Beyond)", Springer-Verlag, New York, 1993. ISBN 0-387-97933-6, ISBN 3-540-97933-6.

2. W. S. Anglin, "The Queen of Mathematics: An Introduction to Number Theory", Kluwer, Dordrecht, 1995. ISBN 0-7923-3287-3.

   W. S. Anglin, American Mathematical Monthly, February 1990, pp. 120-124.

3. Jet Wimp, Eight recent mathematical books, Math. Intelligencer 18 (1996), 72-79.

4. John Baez, Spin and the harmonic oscillator, http://math.ucr.edu/home/baez/harmonic.html

5. David J. Gross, The heterotic string, in "Workshop on Unified String Theories", eds. M. Green and D. Gross, World Scientific, Singapore, 1986, pp. 357-399.

6. Edward Witten, Unification in ten dimensions, in "Workshop on Unified String Theories", eds. M. Green and D. Gross, World Scientific, Singapore, 1986, pp. 438-456.

   Edward Witten, Topological tools in ten dimensional physics, with an appendix by R. E. Stong, in "Workshop on Unified String Theories", eds. M. Green and D. Gross, World Scientific, Singapore, 1986, pp. 400-437.

7. Reinhold W. Gebert and Hermann Nicolai, E10 for beginners, preprint available as hep-th/9411188

8. Gregory Moore, Finite in all directions, preprint available as hep-th/9305139.

9. Reinhold W. Gebert, Introduction to vertex algebras, Borcherds algebras, and the Monster Lie algebra, preprint available as hep-th/9308151.

10. Igor Frenkel, James Lepowsky, and Arne Meurman, "Vertex Operator Algebras and the Monster," Academic Press, 1988.

11. Richard Borcherds, Automorphic forms and Lie algebras.

    Richard Borcherds, Sporadic groups and string theory.

    These and other papers available at http://www.pmms.cam.ac.uk/Staff/R.E.Borcherds.html; click on the personal home page.

12. P. West, E₁₁ and M-theory, available as hep-th/0104081.

week96

1. J. Scott Carter, Daniel E. Flath and Masahico Saito, "The Classical and Quantum 6j-Symbols", Princeton University Press, Princeton, 1995. ISBN 0-691-02730-7.

2. E. Guadagnini, L. Pilo, Three-manifold invariants and their relation with the fundamental group, 22 pages, preprint available as hep-th/9612090.

3. Michael Reisenberger and Carlo Rovelli, "Sum over surfaces" form of loop quantum gravity, preprint available as gr-qc/9612035.

week97

1. Spin, statistics, CPT and all that jazz, http://math.ucr.edu/home/baez/spin.stat.html

2. Physicists create new state of matter, http://jilav1.colorado.edu/www/bose-ein.html

   Atomcool home page, http://atomcool.rice.edu/

   Neutral sodium ion trap at MIT, http://bink.mit.edu/dallin/nat.html

3. Matter-wave interference of two Bose condensates, http://bink.mit.edu/dallin/news.html#matterwave

4. Rodolfo Gambini and Jorge Pullin, "Loops, knots, gauge theories, and quantum gravity", Cambridge U. Press, Cambridge, 1996, ISBN 0-521-47332-2.

5. Gerard 't Hooft, Nucl. Phys. B138, (1978) 1.

6. Abhay Ashtekar and Alejandro Corichi, Gauss linking number and electro-magnetic uncertainty principle, preprint available as hep-th/9701136.

7. Dror Bar-Natan and Alexander Stoimenow, The fundamental theorem of Vassiliev invariants, preprint available as q-alg/9702009.

week98

1. Kirill Krasnov, On statistical mechanics of Schwarzschild black hole, preprint available as gr-qc/9605047.

2. Maximo Banados and Andres Gomberoff, Black hole entropy in the Chern-Simons formulation of 2+1 gravity, preprint available as gr-qc/9611044.

3. John Baez, Degenerate solutions of general relativity from topological field theory, preprint available as gr-qc/9702051 or in Postscript form at http://math.ucr.edu/home/baez/deg.ps.

4. Neil Ashby, General relativity in the global positioning system, in Matters of Gravity, ed. Jorge Pullin, no. 9, available at http://www.phys.lsu.edu//mog/mog9/node9.html.

5. "Handbook of Algebraic Topology", ed. I. M. James, North-Holland, the Netherlands, 1995, 1324 pages, ISBN 0-444-81779-4.

week99

1. Lee Smolin, The future of spin networks, in The Geometric Universe: Science, Geometry, and the Work of Roger Penrose, eds. S. Huggett, Paul Tod, and Lionel J. Mason, Oxford University Press, 1998. Also available as gr-qc/9702030.

2. Roger Penrose, Theory of quantized directions, unpublished manuscript.

3. Fotini Markopoulou and Lee Smolin, Causal evolution of spin networks, preprint available as gr-qc/9702025.

4. Luca Bombelli, Joohan Lee, David Meyer and Rafael D. Sorkin, Space-time as a causal set, Phys. Rev. Lett. 59 (1987), 521.

5. Workshop on Higher Category Theory and Physics, March 28-30, 1997, Northwestern University, Evanston, Illinois. Organized by Ezra Getzler and Mikhail Kapranov; program available at http://math.nwu.edu/~getzler/conf97.html

6. Higher algebraic structures and quantization, by Dan Freed, Comm. Math. Phys. 159 (1994), 343-398, preprint available as hep-th/9212115; see also week48.

7. Louis Crane: Clock and category: is quantum gravity algebraic?, Jour. Math. Phys. 36 (1995), 6180-6193, preprint available as gr-qc/9504038.

8. John Baez, Higher-dimensional algebra II: 2-Hilbert spaces, to appear in Adv. Math., preprint available as q-alg/9609018 or at http://math.ucr.edu/home/baez/2hilb.ps.Z

week100

1. S. Eilenberg and S. Mac Lane, General theory of natural equivalences, Trans. Amer. Math. Soc. 58 (1945), 231-294.

2. J. Benabou, Introduction to bicategories, Springer Lecture Notes in Mathematics 47, New York, 1967, pp. 1-77.

3. R. Gordon, A. J. Power, and R. Street, Coherence for tricategories, Memoirs Amer. Math. Soc. 117 (1995) Number 558.

4. S. E. Crans, On combinatorial models for higher dimensional homotopies, Ph.D. thesis, University of Utrecht, Utrecht, 1991.

5. Ross Street, The algebra of oriented simplexes, Jour. Pure Appl. Alg. 49 (1987), 283-335.

6. J. Baez and J. Dolan, n-Categories - sketch of a definition, letter to Ross Street, Nov. 29, 1995, available at http://math.ucr.edu/home/baez/ncat.def.html

7. J. Baez and J. Dolan, Higher-dimensional algebra III: n-Categories and the algebra of opetopes, to appear in Adv. Math., preprint available as q-alg/9702014 and at http://math.ucr.edu/home/baez/op.ps, or in compressed form as http://math.ucr.edu/home/baez/op.ps.Z

8. Z. Tamsamani, Sur des notions de $\infty$-categorie et $\infty$-groupoide non-strictes via des ensembles multi-simpliciaux, Ph.D. thesis, Universite Paul Sabatier, Toulouse, France, 1995.

9. M. A. Batanin, On the definition of weak omega-category, Macquarie Mathematics Report number 96/207.

week101

1. Manfred Eigen, The Hypercycle, a Principle of Natural Self-Organization, Springer-Verlag, Berlin, 1979.

2. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems: from Dissipative Structures to Order Through Fluctuations, Wiley, New York, 1977.

   Ilya Prigogine, From Being to Becoming: Time and Complexity in the Physical Sciences, W. H. Freeman, San Francisco, 1980.

   Ilya Prigogine, Introduction to Thermodynamics of Irreversible Processes, 3d ed., Interscience Publishers, New York, 1967.

3. Stuart A. Kauffman, At Home in the Universe: the Search for Laws of Self-Organization and Complexity, Oxford University Press, New York, 1995.

   Stuart A. Kauffman, The Origins of Order: Self-Organization and Selection in Evolution, Oxford University Press, New York, 1993.

4. Lee Smolin, The Life of the Cosmos, Crown Press, 1997.

5. Stuart Kauffman and Lee Smolin, A possible solution to the problem of time in quantum cosmology, preprint available as gr-qc/9703026.

6. Edge: http://www.edge.org

week102

1. Ulrike Tillmann, The moduli space of Riemann surfaces - a homotopy theory approach, talk at Northwestern University Algebraic Topology Conference, March 27, 1997

2. Douglas C. Ravenel, Complex cobordism and stable homotopy groups of spheres, Academic Press, Orlando, 1986.

   Douglas C. Ravenel, Nilpotence and periodicity in stable homotopy theory, Princeton University Press, Princeton, 1992.

3. Higher-dimensional algebra and topological quantum field theory, by John Baez and James Dolan, Jour. Math. Phys. 36 (1995), 6073-6105.

week103

1. Ronald Brown, Higher-dimensional group theory, http://www.bangor.ac.uk/~mas010/home.html

2. Symbolic sculptures and mathematics, http://www.bangor.ac.uk/~mas007/welcome.html

3. Ross Street, The role of Michael Batanin's monoidal globular categories. Lecture I: Globular categories and trees. Lecture II: Higher operads and weak omega-categories. Available in gunzipped Postscript form at http://www.math.mq.edu.au/~street/Publications.html

4. Michael Batanin, Monoidal globular categories as a natural environment for the theory of weak n-categories, Adv. Math 136 (1998), 39-103, preprint available at http://www-math.mpce.mq.edu.au/~mbatanin/papers.html

5. John Baez, An introduction to n-categories, to appear in the proceedings of Category Theory and Computer Science '97, preprint available as q-alg/9705009 or in Postscript form at http://math.ucr.edu/home/baez/ncat.ps

6. Zouhair Tamsamani, Sur des notions de $\infty$-categorie et $\infty$-groupoide non-strictes via des ensembles multi-simpliciaux, preprint available as alg-geom/9512006.

   Zouhair Tamsamani, Equivalence de la theorie homotopique des n-groupoides et celle des espaces topologiques n-tronques, preprint available as alg-geom/9607010.

7. Carlos Simpson, A closed model structure for n-categories, internal Hom, n-stacks and generalized Seifert-Van Kampen, preprint available as alg-geom/9704006.

8. J. Scott Carter, Joachim H. Rieger and Masahico Saito, A combinatorial description of knotted surfaces and their isotopies, to appear in Adv. Math., preprint available at http://www.math.usf.edu/~saito/home.html

9. John Baez and Laurel Langford, 2-Tangles, preprint available as q-alg/9703033 and in Postscript form at http://math.ucr.edu/home/baez/2tang.ps

10. J. Scott Carter, Louis H. Kauffman and Masahico Saito, Diagrammatics, singularities, and their algebraic interpretations, preprint available at http://www.math.usf.edu/~saito/home.html

week104

1. Michael J. Crowe, A History of Vector Analysis, University of Notre Dame, Notre Dame, 1967.

2. Tony Smith, http://www.innerx.net/personal/tsmith/TShome.html

3. Geoffrey Dixon, http://www.7stones.com (Warning: to really get into this you need to have at least Netscape 3.0 with Java and Shockwave stuff.)

4. Corinne A. Manogue and Joerg Schray, Finite Lorentz transformations, automorphisms, and division algebras, Jour. Math. Phys. 34 (1993), 3746-3767.

   Corinne A. Manogue and Joerg Schray, Octonionic representations of Clifford algebras and triality, preprint available as hep-th/9407179.

5. Anthony Sudbery, Division algebras, (pseudo)orthogonal groups and spinors, Jour. Phys. A 17 (1984), 939-955.

   Anthony Sudbery, Seven types of incongruity, handwritten notes.

6. J. M. Evans, Supersymmetric Yang-Mills theories and division algebras, Nucl. Phys. B298 (1988), 92-108.

week105

1. The Collected Papers of Raoul Bott, ed. R. D. MacPherson. Vol. 1: Topology and Lie Groups (the 1950s). Vol. 2: Differential Operators (the 1960s). Vol. 3: Foliations (the 1970s). Vol. 4: Mathematics Related to Physics (the 1980s). Birkhauser, Boston, 1994, 2355 pages total.

2. M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology (3) 1964, 3-38.

3. Dave Rusin, Binary products, algebras, and division rings, http://www.math.niu.edu/~rusin/known-math/95/division.alg

week106

1. Boris Rosenfeld, Geometry of Lie Groups, Kluwer Academic Publishers, 1997.

2. John Frank Adams, Lectures on Exceptional Lie Groups, eds. Zafer Mahmud and Mamoru Mimura, University of Chicago Press, Chicago, 1996.

3. Michael B. Green, John H. Schwarz, and Edward Witten, Superstring Theory, two volumes, Cambridge U. Press, Cambridge, 1987.

4. V. S. Varadarajan, Geometry of Quantum Theory, Springer-Verlag, Berlin, 2nd ed., 1985.

5. Stephen L. Adler, Quaternionic Quantum Mechanics and Quantum Fields, Oxford U. Press, Oxford, 1995.

6. Daniel Allcock, Reflection groups on the octave hyperbolic plane, University of Utah Mathematics Department preprint.

7. Arthur L. Besse, Einstein Manifolds, Springer, Berlin, 1987, pp. 313-316.

week107

1. Florian W. J. Weig, Peter V. Coveney, and Bruce M. Boghosian, Lattice- gas simulations of minority-phase domain growth in binary immiscible and ternary amphiphilic fluid, preprint available as cond-mat/9705248.

2. James Gilliam, Lagrangian and Symplectic Techniques in Discrete Mechanics, Ph.D. thesis, Department of Mathematics, University of Riverside, 1996.

   John Baez and James Gilliam, An algebraic approach to discrete mechanics, Lett. Math. Phys. 31 (1994), 205-212. Also available as http://math.ucr.edu./home/baez/ca.tex

3. P. R. Kotiuga, Metric dependent aspects of inverse problems and functionals based helicity, Journal of Applied Physics, 70 (1993), 5437-5439.

   Analysis of finite element matrices arising from discretizations of helicity functionals, Journal of Applied Physics, 67 (1990), 5815-5817.

   Helicity functionals and metric invariance in three dimensions, IEEE Transactions on Magnetics, MAG-25 (1989), 2813-2815.

   Variational principles for three-dimensional magnetostatics based on helicity, Journal of Applied Physics, 63 (1988), 3360-3362.

4. Gerald Jay Sussman and Jack Wisdom, Chaotic evolution of the solar system, Science, 257, 3 July 1992.

   Gerald Jay Sussman and Jack Wisdom, Numerical evidence that the motion of Pluto is chaotic, Science, 241, 22 July 1988.

   James Applegate, M. Douglas, Y. Gursel, Gerald Jay Sussman, Jack Wisdom, The outer solar system for 200 million years, Astronomical Journal, 92, pp 176-194, July 1986, reprinted in Lecture Notes in Physics #267 -- Use of Supercomputers in Stellar Dynamics, Springer Verlag, 1986.

   James Applegate, M. Douglas, Y. Gursel, P Hunter, C. Seitz, Gerald Jay Sussman, A digital orrery, in IEEE Transactions on Computers, C-34, No. 9, pp. 822-831, September 1985, reprinted in Lecture Notes in Physics #267, Springer Verlag, 1986.

5. John Baez, An introduction to n-categories, to appear in 7th Conference on Category Theory and Computer Science, eds. E. Moggi and G. Rosolini, Springer Lecture Notes in Computer Science vol. 1290, Springer, Berlin. Preprint available as q-alg/9705009 or at http://math.ucr.edu/home/baez/ncat.ps

6. Claudio Hermida, Michael Makkai and John Power, On weak higher dimensional categories, 104 pages, preprint available at http://hypatia.dcs.qmw.ac.uk/authors/M/MakkaiM/papers/multitopicsets/

7. Michael Batanin, Finitary monads on globular sets and notions of computad they generate, available as postscript files at http://www-math.mpce.mq.edu.au/~mbatanin/papers.html

8. Carlos Simpson, Limits in n-categories, approximately 90 pages, preprint available as alg-geom/9708010.

9. Sjoerd Crans, Generalized centers of braided and sylleptic monoidal 2-categories, preprint available at http://www-math.mpce.mq.edu.au/~scrans/papers/papers.html

week108

1. Eugenio Moggi and Giuseppe Rosolini, eds., Category Theory and Computer Science, Lecture Notes in Computer Science 1290, Springer Verlag, Berlin, 1997.

2. Michael Reed and Barry Simon, Methods of Modern Mathematical Physics. Vol. 1: Functional Analysis. Vol. 2: Fourier Analysis, Self-Adjointness. Vol. 3: Scattering Theory. Vol. 4: Analysis of Operators. Academic Press, New York, 1980.

3. Andre Joyal, Une th'eorie combinatoire des s'eries formelles, Advances in Mathematics 42 (1981), 1-82.

4. N. Chomsky and M. P. Schutzenberger, The algebraic theory of context-free languages, in Computer Programming and Formal Systems, North-Holland Publishing Company, 1963.

5. Samuel Eilenberg, Automata, Languages and Machines, Academic Press, NY, 1974.

6. Ole Vilhelm Larsen, Computing order-independent statistical characteristics of stochastic context-free languages, available as http://cwis.auc.dk/phd/fulltext/larsen/html/index.html or acrobat format in: http://cwis.auc.dk/phd/fulltext/larsen/pdf/larsen.pdf

week109

1. Charles Misner, Kip Thorne and John Wheeler, Gravitation Freeman Press, 1973.

2. John Wheeler, Geometrodynamics, Academic Press, New York, 1962.

3. Roger Penrose and Wolfgang Rindler, Spinors and Space-Time. Vol. 1: Two-Spinor Calculus and Relativistic Fields. Vol. 2: Spinor and Twistor Methods in Space-Time Geometry. Cambridge University Press, Cambridge, 1985-1986.

4. Robert M. Wald, General Relativity, University of Chicago Press, Chicago, 1984.

5. John Moussouris, Quantum models of space-time based on recoupling theory, Ph.D. thesis, Department of Mathematics, Oxford University, 1983.

6. Edward Witten, A new proof of the positive energy theorem, Commun. Math. Phys. 80 (1981), 381-402.

week110

1. Angular momentum; an approach to combinatorial space time, by Roger Penrose, in Quantum Theory and Beyond; ed. T. Bastin, Cambridge University Press, Cambridge, 1971.

2. Carlo Rovelli, Loop quantum gravity, preprint available as gr-qc/9710008, also available as a webpage on Living Reviews in Relativity at http://www.livingreviews.org/Articles/Volume1/1998-1rovelli/

3. Carlo Rovelli's homepage, http://www.phyast.pitt.edu/~rovelli/

4. Andrea Barbieri, Quantum tetrahedra and simplicial spin networks, preprint available as gr-qc/9707010.

5. C. Nash, Topology and physics - a historical essay, to appear in A History of Topology, edited by Ioan James, Elsevier-North Holland, preprint available as hep-th/9709135.

6. Luis Alvarez-Gaume and Frederic Zamora, Duality in quantum field theory (and string theory), available as hep-th/9709180.

7. Richard E. Borcherds, What is a vertex algebra?, available as q-alg/9709033.

8. J. M. F. Labastida and Carlos Lozano, Lectures in topological quantum field theory, 62 pages, preprint available as hep-th/9709192.

9. Martin Markl, Simplex, associahedron, and cyclohedron, preprint available as alg-geom/9707009.

week111

1. Roger Penrose, Gravitational collapse: the role of general relativity, Rev. del Nuovo Cimento 1, (1969) 272-276.

2. Stephen Hawking, Gravitational radiation from colliding black holes, Phys. Rev. Lett. 26 (1971), 1344-1346.

3. Robert M. Wald, Black holes and thermodynamics, in Symposium on Black Holes and Relativistic Stars (in honor of S. Chandrasekhar), December 14-15, 1996, preprint available as gr-qc/9702022.

4. Jacob Bekenstein, Black holes and entropy, Phys. Rev. D7 (1973), 2333-2346.

5. Stephen Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975), 199-220.

6. Gary Horowitz, Quantum states of black holes, preprint available as gr-qc/9704072.

7. Roman Jackiw, What is quantum field theory and why have some physicists abandoned it?, 4 pages, preprint available as hep-th/9709212.

8. Adel Bilal, M(atrix) theory: a pedagogical introduction, preprint available as hep-th/9710136.

9. Gregory Gabadadze, Modeling the glueball spectrum by a closed bosonic membrane, 43 pages, preprint available as hep-ph/9710402.

10. Jose M. Figueroa-O'Farrill, Gauge theory and the division algebras, preprint available as hep-th/9710168.

week112

1. Greg Egan, Distress, HarperCollins, 1995.

2. Abhay Ashtekar, John Baez, Alejandro Corichi and Kirill Krasnov, Quantum geometry and black hole entropy, to appear in Phys. Rev. Lett., preprint available as gr-qc/9710007.

3. Giorgio Immirzi, Quantum gravity and Regge calculus, in Nucl. Phys. Proc. Suppl. 57 (1997) 65-72, preprint available as gr-qc/9701052.

4. Fernando Barbero, Real Ashtekar variables for Lorentzian signature space-times, Phys. Rev. D51 (1995), 5507-5510, preprint available as gr-qc/9410014.

5. Carlo Rovelli and Thomas Thiemann, The Immirzi parameter in quantum general relativity, preprint available as gr-qc/9705059.

6. Kirill Krasnov, On the constant that fixes the area spectrum in canonical quantum gravity, preprint available as gr-qc/9709058.

7. Kirill Krasnov, Quantum geometry and thermal radiation from black holes, preprint available as gr-qc/9710006.

8. Jacob D. Bekenstein and V. F. Mukhanov, Spectroscopy of the quantum black hole, preprint available as gr-qc/9505012.

9. Jun-ichi Igusa, Theta Functions, Springer-Verlag, Berlin, 1972.

10. David Mumford, Tata Lectures on Theta, 3 volumes, Birkhauser, Boston, 1983-1991.

week113

1. C. Hog-Angeloni, W. Metzler, and A. Sieradski, Two-dimensional Homotopy and Combinatorial Group Theory, London Mathematical Society Lecture Note Series 197, Cambridge U. Press, Cambridge, 1993.

2. John Barrett and Louis Crane, Relativistic spin networks and quantum gravity, 9 pages, preprint available as gr-qc/9709028.

3. John Baez, Spin foam models, 39 pages, preprint available as gr-qc/9709052 or in Postscript form as http://math.ucr.edu/home/baez/foam.ps

4. Michael Reisenberger, Worldsheet formulations of gauge theories and gravity, preprint available as gr-qc/9412035.

5. Michael Reisenberger and Carlo Rovelli, ``Sum over surfaces'' form of loop quantum gravity, Phys. Rev. D56 (1997), 3490-3508, preprint available as gr-qc/9612035.

6. Michael Reisenberger, A lattice worldsheet sum for 4-d Euclidean general relativity, 50 pages, preprint available as gr-qc/9711052.

7. Andrea Barbieri, Space of the vertices of relativistic spin networks, 2 pages, preprint available as gr-qc/9709076.

8. Louis Crane, On the interpretation of relativistic spin networks and the balanced state sum, 4 pages, preprint available as gr-qc/9710108.

week114

1. John W. Barrett, Martin Rocek, Ruth M. Williams, A note on area variables in Regge calculus, preprint available as gr-qc/9710056.

2. Jarmo Makela, Variation of area variables in Regge calculus preprint available as gr-qc/9801022.

3. Louis Crane and David N. Yetter, On the classical limit of the balanced state sum, preprint available as gr-qc/9712087.

4. Lee Smolin, Strings as perturbations of evolving spin-networks, preprint available as hep-th/9801022.

5. Fotini Markopoulou and Lee Smolin, Quantum geometry with intrinsic local causality, preprint available as gr-qc/9712067.

6. Abhay Ashtekar and Jerzy Lewandowski, Quantum theory of geometry II: volume operators, preprint available as gr-qc/9711031.

7. Thomas Thiemann, Quantum spin dynamics (QSD), preprint available as gr-qc/9606089.

   Quantum spin dynamics (QSD) II, preprint available as gr-qc/9606090.

   QSD III: Quantum constraint algebra and physical scalar product in quantum general relativity, preprint available as gr-qc/9705017.

   QSD IV: 2+1 Euclidean quantum gravity as a model to test 3+1 Lorentzian quantum gravity, preprint available as gr-qc/9705018.

   QSD V: Quantum gravity as the natural regulator of matter quantum field theories, preprint available as gr-qc/9705019.

   QSD VI: Quantum Poincare algebra and a quantum positivity of energy theorem for canonical quantum gravity, preprint available as gr-qc/9705020

   Kinematical Hilbert spaces for fermionic and Higgs quantum field theories, gr-qc/9705021

8. Jerzy Lewandowski and Donald Marolf, Loop constraints: A habitat and their algebra, preprint available as gr-qc/9710016.

9. Rodolfo Gambini, Jerzy Lewandowski, Donald Marolf, and Jorge Pullin, On the consistency of the constraint algebra in spin network quantum gravity, preprint available as gr-qc/9710018.

10. Steven Carlip, Spacetime foam and the cosmological constant, Phys. Rev. Lett. 79 (1997) 4071-4074, preprint available as gr-qc/9708026.

week115

1. Greg Egan, Diaspora, Orion Books, 1997.

2. Saunders Mac Lane and Ieke Moerdijk, Sheaves in Geometry and Logic: a First Introduction to Topos Theory, Springer-Verlag, New York, 1992.

3. Saunders Mac Lane, Categories for the Working Mathematician, Springer, Berlin, 1988.

4. J. Peter May, Simplicial Objects in Algebraic Topology, Van Nostrand, Princeton, 1968.

week116

1. Lochlainn O'Raifeartaigh, The Dawning of Gauge Theory, Princeton U. Press, Princeton, 1997.

2. Henri Cartan and Samuel Eilenberg, Homological Algebra, Princeton University Press, 1956.

3. Saunders Mac Lane, Homology, Springer-Verlag, Berlin, 1995.

4. Joseph J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.

5. Marvin J. Greenberg, John R. Harper, Algebraic Topology: A First Course, Benjamin/Cummings, Reading, Massachusetts, 1981.

6. William S. Massey, Singular Homology Theory, Springer-Verlag, New York, 1980.

week117

1. The E864 Collaboration, Search for charged strange quark matter produced in 11.5 A GeV/c Au + Pb collisions, Phys. Rev. Lett. 79 (1997) 3612-3616, preprint available as nucl-ex/9706004.

2. Juergen Eschke, NA35 Collaboration, Strangeness enhancement in sulphur- nucleus collisions at 200 GeV/N, preprint available as hep-ph/9609242.

3. E. P. Gilson and R. L. Jaffe, Very small strangelets, Phys. Rev. Lett. 71 (1993) 332-335, preprint available as hep-ph/9302270.

4. Edward Witten, Cosmic separation of phases, Phys. Rev. D30 (1984) 272-285.

5. Dany Page, Strange stars: Which is the ground state of QCD at finite baryon number?, `High Energy Phenomenology' eds. M. A. Perez & R. Huerta (World Scientific), 1992, pp. 347 - 356, preprint available as astro-ph/9602043.

6. Strange Quark Matter in Physics and Astrophysics: Proceedings of the International Workshop on Strange Quark Matter in Physics and Astrophysics, ed. Jes Madsen, North-Holland, Amsterdam, 1991.

7. International Symposium on Strangeness and Quark Matter, eds. Georges Vassiliadis et al, World Scientific, Singapore, 1995.

8. Graeme B. Segal, Classifying spaces and spectral sequences, Publ. Math. Inst. des Haut. Etudes Scient. 34 (1968), 105-112.

week118

1. Michael J. Duff, The theory formerly known as strings, Scientific American 278 (February 1998), 64-69.

2. M. J. Duff, Supermembranes, preprint available as hep-th/9611203

3. Michael B. Green, John H. Schwarz, and Edward Witten, Superstring Theory, two volumes, Cambridge U. Press, Cambridge, 1987.

4. Bryce DeWitt, Supermanifolds, Cambridge U. Press, Cambridge, 2nd edition, 1992.

5. E. Corrigan and T. J. Hollowood, The exceptional Jordan algebra and the superstring, Commun. Math. Phys., 122 (1989), 393.

6. E. Corrigan and T. J. Hollowood, A string construction of a commutative nonassociative algebra related to the exceptional Jordan algebra, Phys. Lett. B203 (1988), 47.

7. Y. Tanii, Introduction to supergravities in diverse dimensions, preprint available as hep-th/9802138.

8. Stephan Melosch and Hermann Nicolai, New canonical variables for d = 11 supergravity, preprint available as hep-th/9709277.

9. G. Sierra, An application of the theories of Jordan algebras and Freudenthal triple systems to particles and strings, Class. Quant. Grav. 4 (1987), 227.

10. J. M. Evans, Supersymmetric Yang-Mills theories and division algebras, Nucl. Phys. B298 (1988), 92-108.

11. W. Lerche, Recent developments in string theory, preprint available as hep-th/9710246.

12. John Schwarz, The status of string theory, preprint available as hep-th/9711029.

13. M. J. Duff, M-theory (the theory formerly known as strings), preprint available as hep-th/9608117.

week119

1. Edward Witten, Grand unification with and without supersymmetry, Introduction to supersymmetry in particle and nuclear physics, edited by O. Castanos, A. Frank, L. Urrutia, Plenum Press, 1984.

2. Graham G. Ross, Grand Unified Theories, Benjamin-Cummings, 1984.

3. Ranindra N. Mohapatra, Unification and Supersymmetry: The Frontiers of Quark-Lepton Physics, Springer-Verlag, 1992.

4. D. V. Nanopoulos, Tales of the GUT age, in Grand Unified Theories and Related Topics, proceedings of the 4th Kyoto Summer Institute, World Scientific, Singapore, 1981. P. Ramond, Grand unification, in Grand Unified Theories and Related Topics, proceedings of the 4th Kyoto Summer Institute, World Scientific, Singapore, 1981.

5. M. G. Barratt and S. Priddy, On the homology of non-connected monoids and their associated groups, Comm. Math. Helv. 47 (1972), 1-14.

week120

1. Abhay Ashtekar and Kirill Krasnov, Quantum geometry and black holes, preprint available as gr-qc/9804039.

2. Kirill Krasnov, picture of a quantum black hole, http://math.ucr.edu/home/baez/blackhole.eps

3. Louis Crane, David N. Yetter, On the classical limit of the balanced state sum, preprint available as gr-qc/9712087.

4. T. Regge, General relativity without coordinates, Nuovo Cimento 19 (1961), 558-571.

5. David N. Yetter, Generalized Barrett-Crane vertices and invariants of embedded graphs, preprint available as math.QA/9801131.

6. John W. Barrett, The classical evaluation of relativistic spin networks, preprint available at math.QA/9803063.

7. Michael P. Reisenberger, Classical Euclidean general relativity from ``left-handed area = right-handed area'', preprint available as gr-qc/9804061.

8. Roberto De Pietri and Laurent Freidel, so(4) Plebanski action and relativistic spin foam model, preprint available as gr-qc/9804071.

9. Laurent Freidel and Kirill Krasnov, Discrete space-time volume for 3-dimensional BF theory and quantum gravity, preprint available as hep-th/9804185.

10. Ted Jacobson, Black hole thermodynamics today, to appear in Proceedings of the Eighth Marcel Grossmann Meeting, World Scientific, 1998, preprint available as gr-qc/9801015.

11. Rodolfo Gambini, Jorge Pullin, Does loop quantum gravity imply Lambda = 0?, preprint available as gr-qc/9803097.

12. R. Gambini, O. Obregon, and J. Pullin, Yang-Mills analogues of the Immirzi ambiguity, preprint available as gr-qc/9801055.

13. John Baez and Stephen Sawin, Diffeomorphism-invariant spin network states, to appear in Jour. Funct. Analysis, preprint available as q-alg/9708005 or at http://math.ucr.edu/home/baez/int2.ps

14. John H. Schwarz and Nathan Seiberg, String theory, supersymmetry, unification, and all that, to appear in the American Physical Society Centenary issue of Reviews of Modern Physics, March 1999, preprint available as hep-th/9803179.

15. Keith R. Dienes and Christopher Kolda, Twenty open questions in supersymmetric particle physics, 64 pages, preprint available as hep-ph/9712322.

week121

1. Marco Mackaay, Spherical 2-categories and 4-manifold invariants, available as math.QA/9805030

2. John Baez and James Dolan, Categorification, to appear in the Proceedings of the Workshop on Higher Category Theory and Mathematical Physics at Northwestern University, Evanston, Illinois, March 1997, eds. Ezra Getzler and Mikhail Kapranov. Preprint available as math.QA/9802029 or at http://math.ucr.edu/home/baez/cat.ps

3. J. S. Carter and M. Saito, Knotted Surfaces and Their Diagrams, American Mathematical Society, Providence, 1998.

4. Lawrence Breen, Braided n-categories and Sigma-structures, Prepublications Matematiques de l'Universite Paris 13, 98-06, January 1998, to appear in the Proceedings of the Workshop on Higher Category Theory and Mathematical Physics at Northwestern University, Evanston, Illinois, March 1997, eds. Ezra Getzler and Mikhail Kapranov.

5. C. Balteanu, Z. Fiedorowicz, R. Schwaenzl, and R. Vogt, Iterated monoidal categories, available at math.AT/9808082.

6. Representation theory of Hopf categories, Martin Neuchl, Ph.D. dissertation, Department of Mathematics, University of Munich, 1997, available at http://www.mathematik.uni-muenchen.de/~neuchl

7. Jim Stasheff, Grafting Boardman's cherry trees to quantum field theory, available as math.AT/9803156.

8. Masoud Khalkhali, On cyclic homology of A_infinity algebras, available as math.QA/9805051.

   Masoud Khalkhali, Homology of L_infinity algebras and cyclic homology, available as math.QA/9805052.

week122

1. Ivars Peterson, Loops of gravity: calculating a foamy quantum space-time, Science News, June 13, 1998, Vol. 153, No. 24, 376-377.

2. Carlo Rovelli and Peush Upadhya, Loop quantum gravity and quanta of space: a primer, available as gr-qc/9806079.

3. Carlo Rovelli and Merced Montesinos, The fermionic contribution to the spectrum of the area operator in nonperturbative quantum gravity, available as gr-qc/9806120.

4. Carlo Rovelli, Strings, loops and others: a critical survey of the present approaches to quantum gravity. Plenary lecture on quantum gravity at the GR15 conference, Pune, India, available as gr-qc/9803024.

5. Renate Loll, Discrete approaches to quantum gravity in four dimensions, available as gr-qc/9805049, also available as a webpage on Living Reviews in Relativity at http://www.livingreviews.org/Articles/Volume1/1998-13loll/

6. Living Reviews in Relativity, http://www.livingreviews.org

7. J. Ambjorn, Quantum gravity represented as dynamical triangulations, Class. Quant. Grav. 12 (1995) 2079-2134.

8. J. Ambjorn, M. Carfora, and A. Marzuoli, The Geometry of Dynamical Triangulations, Springer-Verlag, Berlin, 1998. Also available electronically as hep-th/9612069 - watch out, this is 166 pages long!

9. J. Ambjorn and R. Loll, Non-perturbative Lorentzian quantum gravity, causality and topology change, preprint available as hep-th/9805108.

10. Dirk Kreimer, Renormalization and knot theory, Journal of Knot Theory and its Ramifications, 6 (1997), 479-581. Preprint available as q-alg/9607022 - beware, this is 103 pages long!

    Dirk Kreimer, On the Hopf algebra structure of perturbative quantum field theories, available as q-alg/9707029.

11. Thomas Krajewski and Raimar Wulkenhaar, On Kreimer's Hopf algebra structure of Feynman graphs, available as hep-th/9805098.

week123

1. Greg Egan, Axiomatic, Orion Books, 1995.

   Greg Egan, Luminous, Orion Books, 1998.

2. Daniel C. Dennett and Douglas R. Hofstadter, The Mind's I: Fantasies and Reflections on Self and Soul, Bantam Books, 1982.

3. Greg Egan, Closer, http://www.eidolon.net/old_site/issue_09/09_closr.htm

4. Greg Egan, Foundations, http://www.netspace.net.au/~gregegan/FOUNDATIONS/index.html

5. Gordon L. Kane, Experimental evidence for more dimensions reported, Physics Today, May 1998, 13-16.

   Paul M. Grant, Researchers find extraordinarily high temperature superconductivity in bio-inspired nanopolymer, Physics Today, May 1998, 17-19.

   Jack Watrous, Ribosomal robotics approaches critical experiments; government agencies watch with mixed interest, Physics Today, May 1998, 21-23.

6. Laurent Freidel and Kirill Krasnov, Spin foam models and the classical action principle, available as hep-th/9807092.

7. Abhay Ashtekar, Alejandro Corichi and Jose A. Zapata, Quantum theory of geometry III: Non-commutativity of Riemannian structures, available as gr-qc/9806041.

8. Andre Hirschowitz, Carlos Simpson, Descente pour les n-champs (Descent for n-stacks), approximately 240 pages, in French, available as math.AG/9807049. math.AG/9807049.

9. Michael Batanin, Computads for finitary monads on globular sets, available at http://www-math.mpce.mq.edu.au/~mbatanin/papers.html

10. Tom Leinster, Structures in higher-dimensional category theory, available at http://www.dpmms.cam.ac.uk/~leinster

11. Alain Connes and Dirk Kreimer, Hopf algebras, renormalization and noncommutative geometry, available as hep-th/9808042.

12. Dirk Kreimer, How useful can knot and number theory be for loop calculations?, Talk given at the workshop "Loops and Legs in Gauge Theories", available as hep-th/9807125.

13. Jack Morava, Quantum generalized cohomology, available as math.QA/9807058 and http://hopf.math.purdue.edu/

14. Satyan L. Devadoss, Tessellations of moduli spaces and the mosaic operad, available as math.QA/9807010.

week124

1. Yuri I. Manin, Reflections on arithmetical physics, in Conformal Invariance and String Theory, eds. Petre Dita and Vladimir Georgescu, Academic Press, 1989.

2. W. Wayt Gibbs, Monstrous moonshine is true, Scientific American, November 1998, 40-41. Also available at http://www.sciam.com/1998/1198issue/1198profile.html.

3. Phillippe Di Francesco, Pierre Mathieu, and David Senechal, Conformal Field Theory, Springer, 1997.

4. Victor Kac, Vertex Algebras for Beginners, American Mathematical Society, University Lecture Series vol. 10, 1997.

5. Joseph Polchinski, String Theory, 2 volumes, Cambridge U. Press, 1998.

6. E. Kiritsis, Introduction to Superstring Theory, 244 pages, to be published by Leuven University Press, available as hep-th/9709062.

7. Quantum Fields and Strings: A Course for Mathematicians, eds. P. Deligne, P. Etinghof, D. Freed, L. Jeffrey, D. Kazhdan, D. Morrison and E. Witten, American Mathematical Society, to appear.

8. Abraham Pais, Maurice Jacob, David I. Olive, and Michael F. Atiyah, Review of Paul Dirac: The Man and His Work, Cambridge U. Press, 1998.

9. Michael Berry, Paul Dirac: the purest soul in physics, Physics World, February 1998, pp. 36-40.

week125

1. David Mumford, Picard groups of moduli problems, in Arithmetical Algebraic Geometry, ed. O. F. G. Schilling, Harper and Row, New York, 1965.

2. Joe Harris and Ian Morrison, Moduli of Curves, Springer-Verlag, New York, 1998.

3. K. Behrend, L. Fantechi, W. Fulton, L. Goettsche and A. Kresch, An Introduction to Stacks, in preparation.

4. D. J. Broadhurst and D. Kreimer, Renormalization automated by Hopf algebra, available as hep-th/9810087.

week126

1. Michael B. Green, John H. Schwarz and Edward Witten, Superstring Theory, 2 volumes, Cambridge University Press.

2. Neal Koblitz, Introduction to Elliptic Curves and Modular Forms, 2nd edition, Springer-Verlag, 1993.

3. G. H. Hardy, Divergent Series, Chelsea Pub. Co., New York, 1991.

4. Eric Weinstein's webpage on the Dedekind eta function, http://www.astro.virginia.edu/~eww6n/math/DedekindEtaFunction.html

week127

1. Lennart Berggren, Jonathan Borwein and Peter Borwein, Pi: A Source Book, Springer-Verlag, New York, 1997.

2. PiHex project, http://www.cecm.sfu.ca/projects/pihex/pihex.html

3. Jean-Benoit Bost, Fibres determinants, determinants regularises, et mesures sur les espaces de modules des courbes complexes, Asterisque 152-153 (1987), 113-149.

4. A. A. Beilinson and Y. I. Manin, The Mumford form and the Polyakov measure in string theory, Comm. Math. Phys. 107 (1986), 359-376.

5. Charles Nash, Differential Topology and Quantum Field Theory, Academic Press, New York, 1991.

6. A. M. Polyakov, Quantum geometry of bosonic strings, Phys. Lett. B103 (1981), 207.

7. Richard E. Borcherds, What is moonshine?, talk given upon winning the Fields medal, preprint available as math.QA/9809110.

8. Peter Goddard, The work of R. E. Borcherds, preprint available as math.QA/9808136.

9. Cartoon by J. F. Cartier, http://www.physik.uni-frankfurt.de/~jr/gif/cartoon/cart 0785.gif

10. R. T. Seeley, Complex powers of an elliptic operator, Proc. Symp. Pure Math. 10 (1967), 288-307.

week128

1. John Archibald Wheeler and Kenneth Ford, Geons, Black Holes, and Quantum Foam: A Life in Physics, Norton, New York, 1998.

2. Steven Carlip, Quantum Gravity in 2+1 Dimensions, Cambridge University Press, 1998. ISBN 0-521-56408-5.

3. Jorge Pullin, editor, Matters of Gravity, vol. 12, available at gr-qc/9809031 and at http://www.phys.lsu.edu//mog

4. John W. Barrett, State sum models for quantum gravity, Penn State relativity seminar, August 27, 1998, audio and text of transparencies available at http://vishnu.nirvana.phys.psu.edu/online/Html/Seminars/Fall1998/Barrett/

5. John W. Barrett and Ruth M. Williams, The asymptotics of an amplitude for the 4-simplex, preprint available as gr-qc/9809032.

6. Justin Roberts, Classical 6j-symbols and the tetrahedron, preprint available as math-ph/9812013.

7. Andrea Barbieri, Space of the vertices of relativistic spin networks, preprint available as gr-qc/9709076.

8. Michael P. Reisenberger, On relativistic spin network vertices, preprint available as gr-qc/9809067.

9. Abhay Ashtekar, Chris Beetle and Steve Fairhurst, Mazatlan lectures on black holes, slides available at http://vishnu.nirvana.phys.psu.edu/online/Html/Conferences/Mazatlan/

10. Abhay Ashtekar, Chris Beetle and S. Fairhurst, Isolated horizons: a generalization of black hole mechanics, preprint available as gr-qc/9812065.

11. Matthias Arnsdorf and R. S. Garcia, Existence of spinorial states in pure loop quantum gravity, preprint available as gr-qc/9812006.

12. Steve Carlip, Black hole entropy from conformal field theory in any dimension, preprint available as hep-th/9812013.

week129

1. Geometry and Quantum Physics lectures, 38th Internationale Universitaetswochen fuer Kern- und Teilchenphysik, http://physik.kfunigraz.ac.at/utp/iukt/iukt_99/iukt99-lect.html

2. Geometry and Quantum Physics, proceedings of the 38th Int. Universitaetswochen fuer Kern- und Teilchenphysik, Schladming, Austria, Jan. 9-16, 1999, eds. H. Gausterer, H. Grosse and L. Pittner, to appear in Lecture Notes in Physics, Springer-Verlag, Berlin.

3. Alain Connes, Noncommutative geometry and reality, J. Math. Phys. 36 (1995), 6194.

week130

1. Special Report: Revolution in Cosmology, Scientific American, January 1999. Includes the articles "Surveying space-time with supernovae" by Craig J. Horgan, Robert P. Kirschner and Nicholoas B. Suntzeff, "Cosmological antigravity" by Lawrence M. Krauss, and "Inflation in a low-density universe" by Martin A. Bucher and David N. Spergel.

2. Nikolas Solomey, The Elusive Neutrino, Scientific American Library, 1997.

3. K. Grotz and H. V. Klapdor, The Weak Interaction in Nuclear, Particle and Astrophysics, Adam Hilger, Bristol, 1990.

4. Klaus Winter, ed., Neutrino Physics, Cambridge U. Press, Cambridge, 1991.

5. Felix Boehm and Petr Vogel, Physics of Massive Neutrinos, Cambridge U. Press, Cambridge, 1987.

6. The neutrino oscillation industry, http://www.hep.anl.gov/NDK/hypertext/nu_industry.html

7. Paul Langacker, Implications of neutrino mass, http://dept.physics.upenn.edu/neutrino/jhu/jhu.html

8. Boris Kayser, Neutrino mass: where do we stand, and where are we going?, preprint available as hep-ph/9810513.

9. GALLEX collaboration, GALLEX solar neutrino observations: complete results for GALLEX II, Phys. Lett. B357 (1995), 237-247.

   Final results of the CR-51 neutrino source experiments in GALLEX, Phys. Lett. B420 (1998), 114-126.

   GALLEX solar neutrino observations: results for GALLEX IV, Phys. Lett. B447 (1999), 127-133.

10. SAGE collaboration, Results from SAGE, Phys. Lett B328 (1994), 234-248.

    The Russian-American gallium experiment (SAGE) CR neutrino source measurement, Phys. Rev. Lett. 77 (1996), 4708-4711.

11. LSND collaboration, Evidence for neutrino oscillations from muon decay at rest, Phys. Rev. C54 (1996) 2685-2708, preprint available as nucl-ex/9605001.

    Evidence for anti-muon-neutrino -> anti-electron-neutrino oscillations from the LSND experiment at LAMPF, Phys. Rev. Lett 77 (1996), 3082-3085, preprint available as nucl-ex/9605003.

    Evidence for muon-neutrino -> electron-neutrino oscillations from LSND, Phys. Rev. Lett. 81 (1998), 1774-1777, preprint available as nucl-ex/9709006.

    Results on muon-neutrino -> electron-neutrino oscillations from pion decay in flight, Phys. Rev. C58 (1998), 2489-2511.

12. Super-Kamiokande collaboration, Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett 81 (1998), 1562-1567, preprint available as hep-ex/9807003.

13. MACRO collaboration, Measurement of the atmospheric neutrino-induced upgoing muon flux, Phys. Lett. B434 (1998), 451-457, preprint available as hep-ex/9807005.

14. IMB collaboration, A search for muon-neutrino oscillations with the IMB detector, Phys. Rev. Lett 69 (1992), 1010-1013.

15. V. Barger, T. J. Weiler, and K. Whisnant, Inferred 4.4 eV upper limits on the muon- and tau-neutrino masses, preprint available as hep-ph/9808367.

16. David O. Caldwell, The status of neutrino mass, preprint available as hep-ph/9804367.

17. Frank Wilczek, Beyond the Standard Model: this time for real, preprint available as hep-ph/9809509.

18. Lilian Hoddeson, Laurie Brown, Michael Riordan and Max Dresden, eds., The Rise of the Standard Model: Particle Physics in the 1960s and 1970s.

19. LSU Super-Kamiokande group homepage, http://beavis.phys.lsu.edu/~superk/

week131

1. Sheldon Lee Glashow, The new frontier, in First Workshop on Grand Unification, eds. Paul H. Frampton, Sheldon L. Glashow and Asim Yildiz, Math Sci Press, Brookline Massachusetts, 1980, pp. 3-8.

2. Feza Gursey, Symmetry breaking patterns in E_6, in First Workshop on Grand Unification, eds. Paul H. Frampton, Sheldon L. Glashow and Asim Yildiz, Math Sci Press, Brookline Massachusetts, 1980, pp. 39-55.

3. Greg Bothun, Modern Cosmological Observations and Problems, Taylor & Francis, London, 1998.

4. Jayant V. Narlikar, Introduction to Cosmology, Cambridge U. Press, Cambridge, 1993.

5. Peter Coles and Francesco Lucchin, Cosmology: The Origin and Evolution of Cosmic Structure, Wiley, New York, 1995.

6. Sandip K. Chakrabarti, ed., Observational Evidence for Black Holes in the Universe, Kluwer, Dordrecht, 1998.

week132

1. John Baez, Higher-dimensional algebra and Planck-scale physics, to appear in Physics Meets Philosophy at the Planck Scale, eds. Craig Callender and Nick Huggett, Cambridge U. Press. Preprint available as gr-qc/9902017.

2. Geraldine Brady and Todd H. Trimble. A string diagram calculus for predicate logic, and C. S. Peirce's system Beta, available at http://people.cs.uchicago.edu/~ brady

   Geraldine Brady and Todd H. Trimble, A categorical interpretation of Peirce's propositional logic Alpha, Jour. Pure and Appl. Alg. 149 (2000), 213-239.

   Geraldine Brady and Todd H. Trimble, The topology of relational calculus.

3. J. Scott Carter, Louis H. Kauffman, and Masahico Saito, Structures and diagrammatics of four dimensional topological lattice field theories, to appear in Adv. Math., preprint available as math.GT/9806023.

4. J. Scott Carter, Daniel Jelsovsky, Selichi Kamada, Laurel Langford and Masahico Saito, Quandle cohomology and state-sum invariants of knotted curves and surfaces, preprint available as math.GT/9903135.

5. Tom Leinster, Structures in higher-dimensional category theory, preprint available at http://www.dpmms.cam.ac.uk/~leinster

6. Claudio Hermida, Higher-dimensional multicategories, slides of a lecture given in 1997, available at http://www.math.mcgill.ca/~hermida

7. Carlos Simpson, On the Breen-Baez-Dolan stabilization hypothesis for Tamsamani's weak n-categories, preprint available as math.CT/9810058.

8. Mark Hovey, Model Categories, American Mathematical Society Mathematical Surveys and Monographs, vol 63., Providence, Rhode Island, 1999.

9. Frank Quinn, Group-categories, preprint available as math.GT/9811047.

10. Sjoerd Crans, A tensor product for Gray-categories, Theory and Applications of Categories, Vol. 5, 1999, No. 2, pp 12-69, available at http://www.tac.mta.ca/tac/volumes/1999/n2/abstract.html

week133

1. Abhay Ashtekar, Quantum Mechanics of Geometry, preprint available as gr-qc/9901023.

2. Fotini Markopoulou, The internal description of a causal set: What the universe looks like from the inside, preprint available as gr-qc/9811053.

   Fotini Markopoulou, Quantum causal histories, preprint available as hep-th/9904009.

3. Seth A. Major, Embedded graph invariants in Chern-Simons theory, preprint available as hep-th/9810071.

4. Lochlainn O'Raifeartaigh, Group structure of gauge theories, Cambridge University Press, Cambridge, 1986.

5. Edward Witten, Search for a realistic Kaluza-Klein theory, Nucl. Phys. B186 (1981), 412-428.

   Edward Witten, Fermion quantum numbers in Kaluza-Klein theory, Shelter Island II, Proceedings: Quantum Field Theory and the Fundamental Problems of Physics, ed. T. Appelquist et al, MIT Press, 1985, pp. 227-277.

6. Thomas Appelquist, Alan Chodos and Peter G. O. Freund, editors, Modern Kaluza-Klein Theories, Addison-Wesley, Menlo Park, California, 1987.

week134

1. Minnowbrook Symposium on Space-Time Structure, program and transparencies of talks available at http://www.phy.syr.edu/research/he_theory/minnowbrook/#PROGRAM

2. Carlo Rovelli, Quantum spacetime: what do we know?, to appear in Physics Meets Philosophy at the Planck Scale, eds. Craig Callender and Nick Huggett, Cambridge U. Press. Preprint available as gr-qc/9903045.

3. J. Butterfield and C. J. Isham, Spacetime and the philosophical challenge of quantum gravity, to appear in Physics Meets Philosophy at the Planck Scale, eds. Craig Callender and Nick Huggett, Cambridge U. Press. Preprint available as gr-qc/9903072.

4. John Baez and John Barrett, The quantum tetrahedron in 3 and 4 dimensions, preprint available as gr-qc/9903060.

5. Abhay Ashtekar, Alejandro Corichi and Kirill Krasnov, Isolated horizons: the classical phase space, preprint available as gr-qc/9905089.

6. Roberto De Pietri, Canonical "loop" quantum gravity and spin foam models, to appear in the proceedings of the XXIIIth Congress of the Italian Society for General Relativity and Gravitational Physics (SIGRAV), 1998, preprint available as gr-qc/9903076.

7. Seth Major, A spin network primer, to appear in Amer. Jour. Phys., preprint available as gr-qc/9905020.

8. Seth Major, Operators for quantized directions, preprint available as gr-qc/9905019.

9. John Baez, An introduction to spin foam models of BF theory and quantum gravity, in Geometry and Quantum Physics, eds. Helmut Gausterer and Harald Grosse, Lecture Notes in Physics, Springer-Verlag, Berlin, 2000, pp. 25-93. Preprint available as gr-qc/9905087.

10. John Barrett and Louis Crane, A Lorentzian signature model for quantum general relativity, preprint available as gr-qc/9904025.

11. Junichi Iwasaki, A surface theoretic model of quantum gravity, preprint available as gr-qc/9903112.

12. Richard E. Borcherds, Quantum vertex algebras, preprint available as math.QA/9903038.

week135

1. Toward a New Understanding of Space, Time and Matter, workshop home page at http://axion.physics.ubc.ca/Workshop/

2. David W. Cohen, An Introduction to Hilbert Space and Quantum Logic, Springer-Verlag, New York, 1989.

3. C. Piron, Foundations of Quantum Physics, W. A. Benjamin, Reading, Massachusetts, 1976.

4. C. A. Hooker, editor, The Logico-algebraic Approach to Quantum Mechanics, two volumes, D. Reidel, Boston, 1975-1979.

5. William Wooters and Wocjciech Zurek, A single quantum cannot be cloned, Nature 299 (1982), 802-803.

6. Classical and Quantum Physics of Strong Gravitational Fields, program homepage with transparencies and audio files of talks at http://www.itp.ucsb.edu/~patrick/gravity99/

7. LIGO project home page, http://www.ligo.caltech.edu/

8. Other gravitational wave detection projects, http://www.ligo.caltech.edu/LIGO_web/other_gw/gw_projects.html

9. Steve Carlip, Entropy from conformal field theory at Killing horizons, preprint available at gr-qc/9906126.

10. Abhay Ashtekar, Christopher Beetle, and Stephen Fairhurst, Mechanics of isolated horizons, preprint available as gr-qc/9907068.

11. Jerzy Lewandowski, Spacetimes admitting isolated horizons, preprint available as gr-qc/9907058.

12. John McKay, Semi-affine Coxeter-Dynkin graphs and $G \subseteq SU_2(C)$, preprint available as math.QA/9907089.

13. Igor Frenkel, Naihuan Jing and Weiqiang Wang, Vertex representations via finite groups and the McKay correspondence, preprint available as math.QA/9907166.

    Quantum vertex representations via finite groups and the McKay correspondence, preprint available as math.QA/9907175.

week136

1. Category Theory 99 website, with abstracts of talks, http://www.mat.uc.pt/~ct99/

2. School on Category Theory and Applications, Coimbra, July 13-17, 199, Textos de Matematica Serie B No. 21, Departamento De Matematica da Universidade de Coimbra. Contains: "n-Categories" by John Baez, "Algebraic theories" by M. Cristina Pedicchio, and "Chu Spaces: duality as a common foundation for computation and mathematics" by Vaughan Pratt.

3. P. Gabriel and F. Ulmer, Lokal praesentierbare Kategorien, Springer Lecture Notes in Mathematics, Berlin, 1971.

4. William Lawvere, Functorial Semantics of Algebraic Theories, Ph.D. Dissertation, University of Columbia, 1963. Summary appears under same title in: Proceedings of the National Academy of Sciences of the USA 50 (1963), 869-872.

5. William Lawvere and Steve Schanuel, Conceptual Mathematics: A First Introduction to Categories, Cambridge U. Press, Cambridge, 1997.

6. Jacques Penon, Approache polygraphique des $\infty$-categories non strictes, in Cahiers Top. Geom. Diff. 40 (1999), 31-79.

week137

1. Michael Mueger, Galois theory for braided tensor categories and the modular closure, preprint available as math.CT/9812040.

2. John Baez, Higher-dimensional algebra II: 2-Hilbert spaces, Adv. Math. 127 (1997), 125-189. Also available as q-alg/9609018.

3. John Baez and James Dolan, Categorification, in Higher Category Theory, eds. Ezra Getzler and Mikhail Kapranov, Contemporary Mathematics vol. 230, AMS, Providence, 1998, pp. 1-36. Also available at math.QA/9802029.

4. A. Bruguieres, Categories premodulaires, modularisations et invariants des varietes de dimension 3, preprint.

5. Stephen Sawin, Jones-Witten invariants for nonsimply-connected Lie groups and the geometry of the Weyl alcove, preprint available as math.QA/9905010.

6. Marco Mackaay, Finite groups, spherical 2-categories, and 4-manifold invariants, preprint available as math.QA/9903003.

7. Mikhail Khovanov, A categorification of the Jones polynomial, preprint available as math.QA/9908171.

8. J. Bernstein, I. Frenkel and M. Khovanov, A categorification of the Temperley-Lieb algebra and Schur quotients of U(sl_2) by projective and Zuckerman functors, to appear in Selecta Mathematica.

9. Mikhail Khovanov, Graphical calculus, canonical bases and Kazhdan-Lusztig theory, Ph.D. thesis, Yale, 1997.

week138

1. James Hartle and Stephen Hawking, Path integral derivation of black hole radiance, Phys. Rev. D13 (1976), 2188.

2. James Hartle and Stephen Hawking, Wavefunction of the universe, Phys. Rev. D28 (1983), 2960.

week139

1. Vipul Periwal, Cosmological and astrophysical tests of quantum gravity, preprint available at astro-ph/9906253

2. John Baez, Renormalization made easy, http://math.ucr.edu/home/baez/renormalization.html

3. Herbert W. Hamber and Ruth M. Williams, Newtonian potential in quantum Regge gravity, Nucl. Phys. B435 (1995), 361-397.

4. Steven Weinberg, Ultraviolet divergences in quantum theories of gravitation, in General Relativity: an Einstein Centenary Survey, eds. Stephen Hawking and Werner Israel, Cambridge U. Press, Cambridge (1979).

5. Steven Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61 (1989), 1.

6. Claude Itzykson and Jean-Michel Drouffe, Statistical Field Theory, 2 volumes, Cambridge U. Press, 1989.

7. Jean Zinn-Justin, Quantum Field Theory and Critical Phenomena, Oxford U. Press, Oxford, 1993.

8. Jan Ambjorn, Bergfinnur Durhuus, and Thordur Jonsson, Quantum Geometry: A Statistical Field Theory Approach, Cambridge U. Press, Cambridge, 1997.

9. Viqar Husain and Sebastian Jaimungal, Phase transition in quantum gravity, preprint available as gr-qc/9908056.

week140

1. Norman Macrae, John von Neumann: The Scientific Genius Who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence and Much More, American Mathematical Society, Providence, Rhode Island, 1999.

2. Steve Batterson, Stephen Smale: The Mathematician Who Broke the Dimension Barrier, American Mathematical Society, Providence, Rhode Island, 2000.

3. Stephen Smale's web page, http://www.math.berkeley.edu/~smale/

4. Roberto De Pietri, Laurent Freidel, Kirill Krasnov, and Carlo Rovelli, Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space, preprint available as hep-th/9907154.

5. Laurent Freidel, Kirill Krasnov and Raymond Puzio, BF description of higher-dimensional gravity, preprint available as hep-th/9901069.

6. Laurent Freidel and Kirill Krasnov, Simple spin networks as Feynman graphs, preprint available as hep-th/9903192.

7. John Barrett and Louis Crane, A Lorentzian signature model for quantum general relativity, preprint available as gr-qc/9904025.

8. Sameer Gupta, Causality in spin foam models, preprint available as gr-qc/9908018.

9. Matthias Arnsdorf and Sameer Gupta, Loop quantum gravity on non-compact spaces, preprint available as gr-qc/9909053.

10. Seth A. Major, Quasilocal energy for spin-net gravity, preprint available as gr-qc/9906052.

11. C. Di Bartolo, R. Gambini, J. Griego, J. Pullin, Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants, preprint available as gr-qc/9909063.

12. John Baez, Spin foam perturbation theory, preprint available as gr-qc/9910050 or at http://math.ucr.edu/home/baez/foam3.ps

week141

1. Chris Mortensen, Inconsistent Mathematics, Kluwer, Dordrecht, 1995.

2. John Milnor, Morse Theory, Princeton U. Press, Princeton, 1960.

3. B. A. Dubrovin, A. T. Fomenko and S. P. Novikov, Modern Geometry - Methods and Applications, Part III: Introduction to Homology Theory, Springer-Verlag Graduate Texts, number 125, Springer, New York, 1990.

4. John Milnor, On manifolds homeomorphic to the 7-sphere, Ann. Math 64 (1956), 399-405.

5. M. Kervaire and J. Milnor, Groups of homotopy spheres I, Ann. Math. 77 (1963), 504-537.

6. J. Levine, Lectures on groups of homotopy spheres, in Algebraic and Geometric Topology, Springer Lecture Notes in Mathematics number 1126, Springer, Berlin, 1985, pp. 62-95.

7. Edward Witten, Global gravitational anomalies, Commun. Math. Phys. 100 (1985), 197-229.

8. Detlef Gromoll and Wolfgang Meyer, An exotic sphere with nonnegative sectional curvature, Ann. Math. 100 (1974), 401-406.

9. Frederick Wilhelm, An exotic sphere with positive curvature almost everywhere, preprint, May 12 1999.

10. Nigel Hitchin, Harmonic spinors, Adv. Math. 14 (1974), 1-55.

11. Reinhard Schultz, Circle actions on homotopy spheres bounding plumbing manifolds, Proc. A.M.S. 36 (1972), 297-300.

12. Louis Kauffman, Knots and Physics, World Scientific, Singapore, 1991.

13. Kristin Schleich and Donald Witt, Exotic spaces in quantum gravity, Class. Quant. Grav. 16 (1999) 2447-2469, preprint available as gr-qc/9903086.

14. Claire Voisin, Mirror Symmetry, American Mathematical Society, 1999.

15. David A. Cox and Sheldon Katz, Mirror Symmetry and Algebraic Geometry, American Mathematical Society, Providence, Rhode Island, 1999.

16. Shing-Tung Yau, editor, Mirror Symmetry I, American Mathematical Society, 1998.

    Brian Green and Shing-Tung Yau, editors, Mirror Symmetry II, American Mathematical Society, 1997.

    Duong H. Phong, Luc Vinet and Shing-Tung Yau, editors, Mirror Symmetry III, American Mathematical Society, 1999.

17. P. Candelas, Lectures on complex manifolds, in Superstrings '87, eds. L. Alvarez-Gaume et al, World Scientific, Singapore, 1988, pp. 1-88.

18. Robert E. Gompf and Andras I Stipsicz, 4-Manifolds and Kirby Calculus, Amderican Mathematical Society, 1999.

19. C. T. C. Wall and A. A. Ranicki, Surgery on Compact Manifolds, 2nd edition, American Mathematical Society, 1999.

20. Alexander A. Voronov, Homotopy Gerstenhaber algebras, preprint available as math.QA/9908040.

21. Maxim Kontsevich, Operads and motives in deformation quantization, Lett. Math. Phys. 48 (1999), 35-72, preprint available as math.QA/9904055.

22. James E. McClure and Jeffrey H. Smith, A solution of Deligne's conjecture, preprint available as math.QA/9910126

week142

1. John Baez, Subcellular life forms, http://math.ucr.edu/home/baez/subcellular.html

2. GNU Go, http://www.gnu.org/software/gnugo/devel.html

3. CGoban, http://www.inetarena.com/~wms/comp/cgoban/

4. American Go Association, http://www.usgo.org/resources/

5. The Nihon Kiin, Go: The World's Most Fascinating Game, 2 volumes, Sokosha Printing Co., Tokyo, 1973.

6. Ishida Yoshio, Dictionary of Basic Joseki, 3 volumes, Ishi Press International, San Jose, California, 1977.

7. Cho Chikun, All About Life and Death, 2 volumes, Ishi Press International, San Jose, California, 1993.

8. Ishidea Yoshio, All About Thickness: Understanding Moyo and Influence, Ishi Press International, San Jose, California.

9. Elwyn Berlekamp and David Wolfe, Mathematical Go: Chilling Gets the Last Point, A. K. Peters, Wellesley Massachusetts, 1994.

10. Markus Enzenberger, The integration of a priori knowledge into a Go playing neural network, http://www.cgl.ucsf.edu/go/Programs/neurogo-html/NeuroGo.html

11. Yasunari Kawabata, The Master of Go, trans. Edward G. Seidensticker, Knopf, New York, 1972.

12. The I Ching or Book of Changes, trans. Richard Wilhelm and Cary F. Baynes, Princeton U. Press, Princeton, 1969.

    The Classic of Changes: A New Translation of the I Ching as Interpreted by Wang Bi, trans. Richard John Lynn, Columbia U. Press, 1994.

13. Henri Darmon, A proof of the full Shimura-Taniyama-Weil conjecture is announced, Notices of the American Mathematical Society, 46 no. 11 (December 1999), 1397-1401.

14. Mikhail Kapranov, Analogies between the Langlands correspondence and topological quantum field theory, in Functional Analysis on the Eve of the 21st Century, Vol. 1, Birkhaueser, Boston, pp. 119-151.

15. M. Makkai, The multitopic omega-category of all multitopic omega-categories, preprint available at ftp://ftp.math.mcgill.ca/pub/makkai

week143

1. Robrt F. Service, Does life's handedness come from within?, Science 286 (November 12, 1999), 1282-1283.

2. Henri Poincare, The present and future of mathematical physics, Bull. Amer. Math. Soc. 12 (1906), 240-260. Reprinted as part of a retrospective issue of the Bull. of the Amer. Math. Soc., 37 (2000), 25-38, available at http://www.ams.org/bull/

3. Carlo Rovelli, The century of the incomplete revolution: searching for general relativistic quantum field theory, to appear in the Journal of Mathematical Physics 2000 Special Issue, preprint available as hep-th/9910131.

4. LIGO homepage, http://www.ligo.caltech.edu/

5. VIRGO homepage, http://www.pi.infn.it/virgo/

6. GEO 600 homepage, http://www.geo600.uni-hannover.de/

7. TAMA 300 homepage, http://tamago.mtk.nao.ac.jp/

8. GRAVITON homepage, http://www.das.inpe.br/graviton/project.html

9. European Space Agency's homepage on the LISA project, http://www.estec.esa.nl/spdwww/future/html/lisa.htm

   NASA's homepage on the LISA project: http://lisa.jpl.nasa.gov/

10. Planck homepage, http://astro.estec.esa.nl/SA-general/Projects/Planck/planck.html

11. Chandra homepage, http://chandra.harvard.edu/

12. XMM homepage, http://sci.esa.int/xmm/

13. MIT's Astro-E homepage, http://acis.mit.edu/syseng/astroe/xis_home.html

14. Robert Irion, Space becomes a physics lab, Science 286 (1999), 2060-2062.

15. Dark Matter Telescope homepage, http://dmtelescope.org

week144

1. M. J. Freyberg and J. Trumper, eds., The Local Bubble and Beyond, proceedings of the IAU Colloquium no. 166, Springer Lecture Notes in Physics 506, Springer-Verlag, Berlin, 1998.

2. Robert Irion, A crushing end for our galaxy, Science 287 (2000), 62-64.

3. Roland Buser, The formation and early evolution of the Milky Way galaxy, Science 287 (2000), 69-74.

4. Chandra resolves cosmic X-ray glow and finds mysterious new sources, press release available online at http://chandra.harvard.edu/press/00_releases/press_011400bg.html

5. James Stasheff, Homotopy associativity of H-spaces I, Trans. Amer. Math. Soc. 108 (1963), 275-292.

   James Stasheff, Homotopy associativity of H-spaces II, Trans. Amer. Math. Soc. 108 (1963), 293-312.

6. James Stasheff, H-spaces from a Homotopy Point of View, Springer Lecture Notes in Mathematics 161, Springer-Verlag, New York, 1970.

7. Robert M. Dickau, Catalan numbers, http://forum.swarthmore.edu/advanced/robertd/catalan.html

8. Kevin Brown, The meanings of Catalan numbers, http://www.seanet.com/~ksbrown/kmath322.htm

9. Herbert Wilf, Generatingfunctionology, Academic Press, Boston, 1994. Also available for free at http://www.cis.upenn.edu/~wilf/

10. Andre Joyal, Une theorie combinatoire des series formelles, Adv. Math. 42 (1981), 1-82.

11. F. Bergeron, G. Labelle, and P. Leroux, Combinatorial species and tree-like structures, Cambridge, Cambridge U. Press, 1998.

12. Richard P. Stanley, Enumerative Combinatorics, volume 2, Cambridge U. Press, Cambridge, 1999, pp. 219-229.

week145

1. V. S. Varadarajan, Geometry of Quantum Mechanics, Springer-Verlag, Berlin, 2nd ed., 1985.

2. Roger Mohr and Bill Trigs, Desargues' Theorem, http://spigot.anu.edu.au/people/samer/Research/Doc/ECV_Tut_Proj_Geom/node25.html

3. Pappus' theorem (a JavaSketchPad demo by MathsNet), http://www.anglia.co.uk/education/mathsnet/dynamic/pappus.html

4. Frederick W. Stevenson, Projective Planes, W. H. Freeman and Company, San Francisco, 1972.

5. Marshall Hall, Projective Planes and Other Topics, California Institute of Technology, Pasadena, 1954.

6. Marshall Hall, The Theory of Groups, Macmillan, New York, 1959.

7. Robin Hartshorne, Foundations of Projective Geometry, Benjamin, New York, 1967.

8. Daniel Pedoe, An Introduction to Projective Geometry, Macmillan, New York, 1963.

9. A. Adrian Albert and Reuben Sandler, An Introduction to Finite Projective Planes, Holt, Rinehart and Winston, New York, 1968.

10. Roger Mohr and Bill Triggs, Projective geometry for image analysis, http://spigot.anu.edu.au/people/samer/Research/Doc/ECV_Tut_Proj_Geom/node1.html

11. J. M. Landsberg and L. Manivel: The projective geometry of Freudenthal's magic square, preprint available as math.AG/9908039.

12. Hans Freudenthal, Lie groups in the foundations of geometry, Adv. Math. 1 (1964) 143.

13. Jacques Tits, Algebres alternatives, algebres de Jordan et algebres de Lie exceptionelles, Proc. Colloq. Utrecht, vol. 135, 1962.

14. R. D. Schafer, Introduction to Non-associative Algebras, Academic Press, 1966.

15. C. H. Barton and A. Sudbery, Magic squares of Lie algebras, preprint available as math.RA/0001083.

week146

1. Max Tegmark, Is the "theory of everything" merely the ultimate ensemble theory?, Ann. Phys. 270 (1998), 1-51, preprint available as gr-qc/9704009.

   Max Tegmark, Which mathematical structure is isomorphic to the universe?, http://www.hep.upenn.edu/~max/toe.html

   Marcus Chown, Anything goes, New Scientist 158 (1998) 26-30, also available at http://www.hep.upenn.edu/~max/toe_press.html

2. J. Ambjorn, J. Correia, C. Kristjansen, and R. Loll, On the relation between Euclidean and Lorentzian 2d quantum gravity, preprint avilable as hep-th/9912267.

   J. Ambjorn, J. Jurkiewicz and R. Loll, Lorentzian and Euclidean quantum gravity - analytical and numerical results, preprint available as hep-th/0001124.

   J. Ambjorn, J. Jurkiewicz and R. Loll, A non-perturbative Lorentzian path integral for gravity, preprint avilable as hep-th/0002050.

3. Abhay Ashtekar, Donald Marolf, Jose Mourao and Thomas Thiemann, Osterwalder-Schrader reconstruction and diffeomorphism invariance, preprint available as quant-ph/9904094.

4. Abhay Ashtekar, Interface of general relativity, quantum physics and statistical mechanics: some recent developments, to appear in Annalen der Physik, preprint available as gr-qc/9910101.

5. Abhay Ashtekar, Alejandro Corichi, and Kirill Krasnov, Isolated horizons: the classical phase space, preprint available as gr-qc/9905089.

   Abhay Ashtekar, Christopher Beetle, and Stephen Fairhurst, Mechanics of isolated horizons, Class. Quant. Grav. 17 (2000) 253-298, preprint available as gr-qc/9907068.

   Abhay Ashtekar and Alejandro Corichi, Laws governing isolated horizons: inclusion of dilaton couplings, preprint available as gr-qc/9910068.

   Jerzy Lewandowski, Space-times admitting isolated horizons, preprint available as gr-qc/9907058.

6. Michael Reisenberger and Carlo Rovelli, Spin foams as Feynman diagrams, preprint available as gr-qc/0002083.

7. Michael Reisenberger and Carlo Rovelli, Spacetime as a Feynman diagram: the connection formulation, preprint available as gr-qc/0002095.

8. Cayetano Di Bartolo, Rodolfo Gambini, Jorge Griego, and Jorge Pullin, Consistent canonical quantization of general relativity in the space of Vassiliev invariants, preprint available as gr-qc/9909063.

   Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure, preprint available as gr-qc/9911009.

   Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra, preprint available as gr-qc/9911010.

9. Martin Bojowald, Loop Quantum Cosmology I: Kinematics, preprint available as gr-qc/9910103.

   Martin Bojowald, Loop Quantum Cosmology II: Volume Operators, gr-qc/9910104.

week147

1. Mathematics: Frontiers and Perspectives, edited by Vladimir Arnold, Michael Atiyah, Peter Lax and Barry Mazur, AMS, Providence, Rhode Island, 2000.

2. Mathematics Unlimited: 2001 and Beyond, edited by Bjorn Engquist and Wilfried Schmid, Springer Verlag, New York, 2000.

3. The American Physical Society: A Century of Physics, available at http://timeline.aps.org/APS/home_HighRes.html

4. John Baez and James Dolan, From finite sets to Feynman diagrams, preprint available as math.QA/0004133

5. James Propp and David Feldman, Producing new bijections from old, Adv. Math. 113 (1995), 1-44. Also available at http://www.math.wisc.edu/~propp/articles.html

6. John Conway and Peter Doyle, Division by three. http://math.dartmouth.edu/~doyle/docs/three/three/three.html

7. Daniel Loeb, Sets with a negative number of elements, Adv. Math. 91 (1992), 64-74.

8. S. Schanuel, Negative sets have Euler characteristic and dimension, Lecture Notes in Mathematics 1488, Springer Verlag, Berlin, 1991, pp. 379-385.

9. James Propp, Exponentiation and Euler measure, available as math.CO/0204009.

10. Andre Joyal, Regle des signes en algebre combinatoire, Comptes Rendus Mathmatiques de l'Academie des Sciences, La societe royale du Canada, VII (1985), 285-290.

11. Matthias Blau and George Thompson, N = 2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant, Comm. Math. Phys. 152 (1993), 41-71.

12. Claudio Hermida, From coherent structures to universal properties, available at http://www.cs.math.ist.utl.pt/cs/s84/claudio.html

13. K. A. Hardie, K. H. Kamps, R. W. Kieboom, A homotopy bigroupoid of a topological space, in: Categorical Methods in Algebra and Topology, pp. 209-222, Mathematik-Arbeitspapiere 48, Universitaet Bremen, 1997. Appl. Categ. Structures, to appear.

    K. A. Hardie, K. H. Kamps, R. W. Kieboom, A homotopy 2-groupoid of a Hausdorff space, preprint.

14. William J. Floyd and Steven P. Plotnick, Growth functions on Fuchsian groups and the Euler characteristic, Invent. Math. 88 (1987), 1-29.

15. R. I. Grigorchuk, Growth functions, rewriting systems and Euler characteristic, Mat. Zametki 58 (1995), 653-668, 798.

16. John Baez, Euler characteristic versus homotopy cardinality, lecture at the Fields Institute Program on Applied Homotopy Theory, September 20, 2003. Available in PDF form at http://www.math.ucr.edu/home/baez/cardinality/

week148

1. Clay Mathematics Institute, Millennium Prize Problems, http://www.claymath.org/prizeproblems/index.htm

2. Abhay Ashtekar, John Baez and Kirill Krasnov, Quantum geometry of isolated horizons and black hole entropy, preprint available at gr-qc/0005126 or at http://math.ucr.edu/home/baez/black2.ps

3. John Wheeler, It from bit, in Sakharov Memorial Lecture on Physics, Volume 2, eds. L. Keldysh and V. Feinberg, Nova Science, New York, 1992.

4. Abhay Ashtekar, Alejandro Corichi and Kirill Krasnov, Isolated horizons: the classical phase space, Advances in Theoretical and Mathematical Physics 3 (2000), 418-471. Preprint available at gr-qc/9905089.

5. Abhay Ashtekar, Chris Beetle and Steve Fairhurst, Mechanics of isolated horizons, Class. and Quant. Gravity 17 (2000), 253-298. Preprint available at gr-qc/9907068.

6. Stephen Smale, Mathematical problems for the next century, Mathematical Intelligencer, 20 (1998), 7-15. Also available in Postscript and PDF as item 104 on Smale's webpage, http://www.cityu.edu.hk/ma/staff/smale/bibliography.html

week149

1. Graeme Segal, Elliptic cohomology, Asterisque 161-162 (1988), 187-201.

2. Peter S. Landweber, editor, Elliptic Curves and Modular Forms in Algebraic Topology, Springer-Verlag Lecture Notes in Mathematics 1326, Springer, Berlin, 1988.

3. Charles B. Thomas, Elliptic Cohomology, Kluwer, Dordrecht, 1999.

4. Edward Witten, Elliptic genera and quantum field theory, Comm. Math. Phys. 109 (1987), 525-536.

5. Friedrich Hirzebruch, Thomas Berger and Rainer Jung, Manifolds and Modular Forms, translated by Peter S. Landweber, Vieweg, Braunschweig (a publication of the Max Planck Institute for Mathematics in Bonn), 1992.

6. J. Adams, Infinite Loop Spaces, Princeton U. Press, Princeton, 1978.

7. J. Adams, Stable Homotopy and Generalized Homology, Chicago Lectures in Mathematics, U. Chicago Press, Chicago, 1974.

8. J. P. May, The Geometry of Iterated Loop Spaces, Lecture Notes in Mathematics 271, Springer Verlag, Berlin, 1972.

9. J. P. May, F. Quinn, N. Ray and J. Tornehave, E_infinity Ring Spaces and E_infinity Ring Spectra, Lecture Notes in Mathematics 577, Springer Verlag, Berlin, 1977.

10. G. Carlsson and R. Milgram, Stable homotopy and iterated loop spaces, in Handbook of Algebraic Topology, ed. I. M. James, North-Holland, 1995.

11. C. N. Yang, Magnetic monopoles, fiber bundles and gauge field, in Selected Papers, 1945--1980, with Commentary, W. H. Freeman and Company, San Francisco, 1983.

12. Dusa McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975), 91-107.

13. Ross H. Street, The petit topos of globular sets, Macquarie Mathematics Report Number 98/232, March 1998.

14. Ross H. Street and Michael Batanin, The universal property of the multitude of trees, Macquarie Mathematics Report Number 98/233, March 1998.

15. Michael Batanin, Shuffle polytopes, cooperative games and 2-dimensional coherence for higher dimensional categories.

week150

1. Lagrange points, http://map.gsfc.nasa.gov/html/lagrange.html

2. Neil J. Cornish, The Lagrange points, available at http://www.astro.princeton.edu/~njc/lagrange.ps.gz

3. Asteroid belt, http://www-groups.dcs.st-and.ac.uk/~history//Diagrams/Asteroids.gif

4. Minor Planet Center, Trojan minor planets, http://cfa-www.harvard.edu/cfa/ps/lists/Trojans.html

5. Paul Wiegert, Kimmo Innanen and Seppo Mikkola, Near-earth asteroid 3753 Cruithne - Earth's curious companion, http://www.astro.queensu.ca/~wiegert/

6. Paul Schlyter, Hypothetical planets, http://seds.lpl.arizona.edu/nineplanets/nineplanets/hypo.html

7. Astronomy picture of the day: Dione's Lagrange moon Helene, http://antwrp.gsfc.nasa.gov/apod/ap951010.html

8. Bill Arnett, Introduction to the nine planets: Tethys, Telesto and Calypso, http://seds.lpl.arizona.edu/nineplanets/nineplanets/tethys.html

9. SOHO website, http://sohowww.nascom.nasa.gov/

10. MAP website, http://map.gsfc.nasa.gov/

11. T. Uzer, Ernestine A. Lee, David Farrelly, and Andrea F. Brunello, Synthesis of a classical atom: wavepacket analogues of the Trojan asteroids, Contemp. Phys. 41 (2000), 1-14. Abstract available at http://www.catchword.co.uk/titles/tandf/00107514/v41n1/contp1-1.htm

12. Dale Husemoller, Fibre Bundles, Springer-Verlag, New York, 1975.

13. H. Blaine Lawson, Jr. and Marie-Louise Michelsohn, Spin Geometry, Princeton University Press, Princeton, 1989.

14. Robert E. Stong, Notes on Cobordism Theory, Princeton University Press, Princeton, 1968.

15. P. E. Conner and E. E. Floyd, The Relation of Cobordism to K-theories, Lecture Notes in Mathematics 28, Springer-Verlag, New York, 1966.

16. Douglas C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, 1986.

17. Hirotaka Tamanoi, Elliptic Genera and Vertex Operator Super-Algebras, Springer Lecture Notes in Mathematics 1704, Springer, Berlin, 1999.

week151

1. Colin Gough, Science and the Stradivarius, Physics World, vol. 13 no. 4, April 2000, 27-33.

2. A. H. Benade, Fundamentals of Musical Acoustics, Oxford University Press, Oxford, 1976.

   L. Cremer, The Physics of the Violin, MIT Press, Cambridge, Massachusetts, 1984.

   N. H. Fletcher and T. D. Rossing, The Physics of Musical Instruments, 2nd edition, Springer, New York, 1998.

   C. Hutchins and V. Benade, editors, Research Papers on Violin Acoustics 1975-1993, 2 volumes, Acoustical Society of America, New York, 1997.

3. Dusa McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975), 91-107.

4. Alan L. Carey, Diarmuid Crowley and Michael K. Murray, Principal bundles and the Dixmier-Douady class, Comm. Math. Physics 193 (1998) 171-196, also available as hep-th/9702147.

5. Pawel Gajer, Geometry of Deligne cohomology, Invent. Math. 127 (1997), 155-207, also available as alg-geom/9601025.

   Pawel Gajer, Higher holonomies, geometric loop groups and smooth Deligne cohomology, Advances in Geometry, Birkhauser, Boston, 1999, pp. 195-235.

6. Jean-Luc Brylinski, Loop Spaces, Characteristic Classes and Geometric Quantization, Birkhauser, Boston, 1993. ISBN 0-176-3644-7

7. Lawrence Breen, On the Classification of 2-Gerbes and 2-Stacks, Asterisque 225, 1994.

8. Alan L. Carey and Michael K. Murray, Faddeev's anomaly and bundle gerbes, Lett. Math. Phys. 37 (1996), 29-36.

   Jouko Mickelsson, Gerbes and Hamiltonian quantization of chiral fermions, Lie Theory and Its Applications in Physics, World Scientific, Singapore, 1996, pp. 216-225.

   Michael K. Murray, Bundle gerbes, J. London Math. Soc. 54 (1996), 403-416.

   Alan L. Carey, Jouko Mickelsson and Michael K. Murray, Index theory, gerbes, and Hamiltonian quantization, Comm. Math. Phys. 183 (1997), 707-722, preprint available as hep-th/9511151.

   Alan L. Carey, Michael K. Murray and B. L. Wang, Higher bundle gerbes and cohomology classes in gauge theories, J. Geom. Phys. 21 (1997) 183-197, preprint available as hep-th/9511169.

   Alan L. Carey, Jouko Mickelsson and Michael K. Murray, Bundle gerbes applied to quantum field theory, Rev. Math. Phys. 12 (2000), 65-90, preprint available as hep-th/9711133.

week152

1. Michael J. Crowe, A History of Vector Analysis, University of Notre Dame Press, Notre Dame, 1967.

2. John Baez, Some thoughts on the number six, http://math.ucr.edu/home/baez/six.html

3. Thomas L. Hankins, Sir William Rowan Hamilton, John Hopkins University Press, Baltimore, 1980.

4. Robert Perceval Graves, Life of Sir William Rowan Hamilton, 3 volumes, Arno Press, New York 1975.

5. W. R. Hamilton, Four and eight square theorems, Appendix 3 of vol. III of The Mathematical Papers of William Rowan Hamilton, eds. H. Halberstam and R. E. Ingram, Cambridge University Press, Cambridge, 1967.

6. L. E. Dickson, On quaternions and their generalization and the history of the eight square theorem, Ann. Math. 20 (1919), 155-171.

7. Heinz-Dieter Ebbinghaus et al, Numbers, Springer, New York, 1990.

week153

1. Reviel Netz, The origins of mathematical physics: new light on an old question, Physics Today, June 2000, 32-37.

2. The Walters Art Gallery, Archimedes Palimpsest website, http://www.thewalters.org/archimedes/frame.html

3. Chris Rorres, Archimedes website, http://www.mcs.drexel.edu/~crorres/Archimedes/contents.html

4. Raoul Bott, Lectures on K(X), Harvard University, Cambridge, 1963.

5. Michael Atiyah, K-theory, W. A. Benjamin, New York, 1967.

6. Max Karoubi, K-theory: an Introduction, Springer, Berlin, 1978.

7. Graeme Segal, Elliptic cohomology, Asterisque 161-162 (1988), 187-201.

8. Hirotaka Tamanoi, Elliptic Genera and Vertex Operator Super-Algebras, Springer Lecture Notes in Mathematics 1704, Springer, Berlin, 1999.

week154

1. Hoi-Kwong Lo, Will quantum cryptography ever become a successful technology in the marketplace?, preprint available as quant-ph/9912011

2. John Preskill, Lecture notes on quantum computation and quantum information theory, available at http://www.theory.caltech.edu/people/preskill/ph229

3. Juan Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231-252, preprint available as hep-th/9711200.

4. Nathan Seiberg and Edward Witten, Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory, Nucl. Phys. B426 (1994) 19-52, preprint available as hep-th/9407087.

5. Edward Witten, String theory dynamics in various dimensions, Nucl. Phys. B443 (1995) 85-126, preprint available as hep-th/9503124.

6. Edward Witten, Anti-DeSitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253-291, preprint available as hep-th/9802150.

7. S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B428 (1998) 105-114, preprint available as hep-th/9802109.

8. Joseph Polchinski, Dirichlet branes and Ramond-Ramond charges, Phys. Rev. Lett. 75 (1995) 4724-4727, preprint available as hep-th/9510017.

9. Nathan Seiberg and Edward Witten, Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD, Nucl. Phys. B431 (1994) 484-550, preprint available as hep-th/9408099.

10. T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, M-theory as a matrix model: a conjecture, Phys. Rev. D55 (1997), 5112-5128, preprint available as hep-th/9610043.

11. C. M. Hull and P. K. Townsend, Unity of superstring dualities, Nucl. Phys. B438 (1995) 109-137, preprint available as hep-th/9410167.

12. Edward Witten, Bound states of strings and p-branes, Nucl. Phys. B460 (1996), 335-350, preprint available as hep-th/9510135.

13. Searching top cited papers on SPIRES, at http://www.slac.stanford.edu/spires/hep/topcite.html

14. P. Budinich and A. Trautman, The Spinorial Chessboard, Springer-Verlag, Berlin, 1988.

15. Claude Chevalley, The Algebraic Theory of Spinors, Springer, Berlin, 1991.

16. Eli Cartan, The Theory of Spinors, Dover Press, 1966.

17. Pertti Lounesto, Clifford Algebras and Spinors, Cambridge U. Press, Cambridge, 1997.

18. Dominic Joyce, Compact Manifolds with Special Holonomy, Oxford U. Press, Oxford, 2000.

19. O. Aharony, S. S. Gubser, J. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183-386, preprint available as hep-th/9905111.

20. Clifford V. Johnson, D-brane primer, preprint available as hep-th/0007170.

21. G. Papadopoulos and P. K. Townsend, Compactification of D=11 supergravity on spaces of exceptional holonomy, preprint available as hep-th/9506150.

22. B. S. Acharya, N=1 heterotic-supergravity duality and Joyce manifolds, preprint available as hep-th/9508046.

    N=1 heterotic/M-theory duality and Joyce manifolds, preprint available as hep-th/9603033.

    N=1 M-theory-heterotic duality in three dimensions and Joyce manifolds, preprint available as hep-th/9604133.

    Dirichlet Joyce manifolds, discrete torsion and duality, preprint available as hep-th/9611036.

    M theory, Joyce orbifolds and super Yang-Mills, preprint available as hep-th/9812205.

23. Chien-Hao Liu, On the global structure of some natural fibrations of Joyce manifolds, preprint available as hep-th/9809007.

week155

1. Acme Klein bottles sliced in half, http://www.kleinbottle.com/sliced_klein_bottles.htm

2. H. S. M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973.

   Regular Complex Polytopes, 2nd edition, Cambridge U. Press, Cambridge, 1991.

3. Eric Weisstein, stella octangula, http://mathworld.wolfram.com/StellaOctangula.html

4. Eric Weisstein, cube 5-compound, http://mathworld.wolfram.com/Cube5-Compound.html

5. Eric Weisstein, tetrahedron 5-compound, http://mathworld.wolfram.com/Tetrahedron5-Compound.html

6. Eric Weisstein, tetrahedron 10-compound, http://mathworld.wolfram.com/Tetrahedron10-Compound.html

7. John Baez, Some thoughts on the number 6, http://math.ucr.edu/home/baez/six.html

8. John Baez, Platonic solids in all dimensions, http://math.ucr.edu/home/baez/platonic.html

9. Eric Weisstein, 24-cell, http://mathworld.wolfram.com/24-Cell.html

10. Kevin Brown, Kepler's rhombic dodecahedron, http://www.seanet.com/~ksbrown/coinc2.htm

11. Mark Newbold's rhombic dodecahedron page, http://dogfeathers.com/mark/rhdodec.html

12. Eric Weisstein, 600-cell, http://mathworld.wolfram.com/600-Cell.html

13. George W. Hart's Pavilion of Polyhedrality, http://www.georgehart.com/pavilion.html

14. Victor Bulatov's Polyhedra Collection, http://www.physics.orst.edu/~bulatov/polyhedra/index.html

15. Tony Smith, 24-cell animation, 120-cell, 600-cell, http://www.innerx.net/personal/tsmith/24anime.html

week156

1. John Kormendy, Monsters at the heart of galaxy formation, Science 289 (2000), 1484-1485. Available online at http://www.sciencemag.org/cgi/content/full/289/5484/1484

2. Laura Ferrarese and David Merritt, A fundamental relation between supermassive black holes and their host galaxies, Astrophys. J. Lett., 539, (2000) L9, preprint available as astro-ph/0006053.

3. Karl Gebhardt et al, A relationship between nuclear black hole mass and galaxy velocity dispersion, Astrophys. J. Lett. 539, (2000) L13, preprint available as astro-ph/0006289.

4. Supermassive Black Hole Group, Theory of black holes and galaxies, http://www.physics.rutgers.edu/~merritt/theory.htm

5. Ed Colbert's homepage, http://www.pha.jhu.edu/~colbert/

   E. J. M. Colbert and R. F. Mushotzky, The nature of accreting black holes in nearby galaxy nuclei, preprint available as astro-ph/9901023.

6. A. Ptak, R. Griffiths, Hard X-ray variability in M82: evidence for a nascent AGN?, preprint available as astro-ph/9903372.

7. David Ceperley et al, Prospective superfluid molecular hydrogen, http://www.aip.org/physnews/graphics/html/h2.htm

8. Slava Grebenev, Boris Sartakov, J. Peter Toennies, and Andrei F. Vilesov, Evidence for superfluidity in para-hydrogen clusters inside helium-4 droplets at 0.15 Kelvin, Science 5484 (2000), 1532-1535, available online at http://www.sciencemag.org/cgi/content/abstract/289/5484/1532

9. R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That, Addison-Wesley, Reading, Massachusetts, 1989.

10. CPLEAR homepage, http://cplear.web.cern.ch/cplear/Welcome.html

    CPLEAR collaboration, First direct observation of time-reversal non-invariance in the neutral kaon system, Phys. Lett. B 444 (1998) 43, available online with all other papers by this collaboration at http://cplear.web.cern.ch/cplear/cplear_pub.html

11. Christina Hebert, Phyisicists find first direct evidence for tau neutrino at Fermilab, http://www.fnal.gov/directorate/public_affairs/story_neutrino/p1.html

12. LEP shutdown postponed by one month, http://press.web.cern.ch/Press/Releases00/PR08.00ELEPRundelay.html

13. Higgs Working Group webpage, http://fnth37.fnal.gov/higgs/higgs.html

14. John Baez, Symplectic, quaternionic, fermionic, http://math.ucr.edu/home/baez/symplectic.html

week157

1. Hermann Weyl, The Classical Groups, Their Invariants and Representations, Princeton U. Press, Princeton, 1997.

2. Irene Verona Schensted, A Course on the Applications of Group Theory to Quantum Mechanics, NEO Press, Box 32, Peaks Island, Maine.

3. Shlomo Sternberg, Group Theory and Physics, Cambridge U. Press, Cambridge, 1994.

4. Gordon Douglas James and Adalbert Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, Reading, Massachusetts, 1981.

6. Roe Goodman and Nolan R. Wallach, Representations and Invariants of the Classical Groups, Cambridge University Press, Cambridge, 1998.

7. William Fulton, Young Tableaux: With Applications to Representation Theory and Geometry, Cambridge U. Press, Cambridge, 1997.

8. William Fulton, Eigenvalues, invariant factors, highest weights, and Schubert calculus, Bull. Amer. Math. Soc. 37 (2000), 209-249, also available as math.AG/9908012.

9. Allen Knutson and Terence Tao, The honeycomb model of GL(n) tensor products I: the saturation conjecture, preprint available as math.RT/9807160

10. Allen Knutson, The symplectic and algebraic geometry of Horn's problem, preprint available as math.LA/9911088.

11. Allen Knutson and Terence Tao, Honeycombs and sums of Hermitian matrices, preprint available as math.RT/0009048

week158

1. The World in Eleven Dimensions: Supergravity, Supermembranes and M-theory, ed. M. J. Duff, Institute of Physics Publishing, Bristol, 1999.

2. Edward Witten, Search for a realistic Kaluza-Klein theory, Nucl. Phys. B186 (1981), 412-428.

3. Quantum Fields and Strings: A Course for Mathematicians, 2 volumes, eds. P. Deligne, P. Etinghof, D. Freed, L. Jeffrey, D. Kazhdan, D. Morrison and E. Witten, American Mathematical Society, Providence, Rhode Island, 1999.

4. W. Nahm, Supersymmetries and their representations, Nucl. Phys. B135 (1978), 149-166.

5. T. Kugo and P. Townsend, Supersymmetry and the division algebras, Nucl. Phys. B221 (1983), 357-380.

6. G. Sierra, An application of the theories of Jordan algebras and Freudenthal triple systems to particles and strings, Class. Quant. Grav. 4 (1987) 227.

7. J. M. Evans, Supersymmetric Yang-Mills theories and division algebras, Nucl. Phys. B298 (1988), 92.

8. M. J. Duff, Supermembranes: the first fifteen weeks, Class. Quant. Grav. 5 (1988), 189-205.

9. Feza Gursey and Chia-Hsiung Tze, On the Role of Division, Jordan, and Related Algebras in Particle Physics, World Scientific, Singapore, 1996.

10. Jaak Lohmus, Eugene Paal and Leo Sorgsepp, Nonassociative Algebras in Physics, Hadronic Press, Palm Harbor, Florida, 1994.

week159

1. Yi Ling and Lee Smolin, Eleven dimensional supergravity as a constrained topological field theory, available as hep-th/0003285.

2. M. J. Plebanski, On the separation of Einsteinian substructures, J. Math. Phys. 18 (1977), 2511.

3. Pietro Fre, Comments on the six index photon in D = 11, preprint TH-3884-CERN.

4. R. D'Auria and P. Fre, Geometric supergravity in D = 11 and its hidden supergroup, Nucl. Phys. B201 (1982), 101. Erratum, Nucl. Phys. B206 (182), 496.

5. L. Castellani, P. Fre and P. van Nieuwenhuizen, A review of the group manifold approach and its applications to conformal supergravity, Ann. Phys. 136 (1981), 398.

6. Martin Cederwall, Ulf Gran, Mikkel Nielsen, and Bengt Nillson, Generalised 11-dimensional supergravity, available as hep-th/0010042.

week160

1. Ralph D. Lorenz, The weather on Titan, Science 290 (October 20, 2000), 467-468.

   Caitlin A. Griffith, Joseph L. Hall and Thomas R. Geballe, Detection of daily clouds on Titan, Science 290 (October 20, 2000), 509-513.

2. Richard A. Kerr, Neptune may crush methane into diamonds, Science 286 (October 1, 1999), 25.

   Laura Robin Benedetti, Jeffrey H. Nguyen, Wendell A. Caldwell, Hongjian Liu, Michael Kruger, and Raymond Jeanloz, Dissociation of CH₄ at high pressures and temperatures: diamond formation in giant planet interiors?, Science 286 (October 1, 1999), 100-102.

3. Science Magazine, http://www.sciencemag.org/search.dtl

4. Alejandro Perez and Carlo Rovelli, A spin foam model without bubble divergences, available as gr-qc/0006107.

5. Alejandro Perez and Carlo Rovelli, Spin foam model for Lorentzian general relativity, available as gr-qc/0009021.

6. Alejandro Perez and Carlo Rovelli, 3+1 spinfoam model of quantum gravity with spacelike and timelike components, available as gr-qc/0011037.

7. Daniele Oriti and Ruth M. Williams, Gluing 4-simplices: a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity, available as gr-qc/0010031.

8. Carlo Rovelli, Notes for a brief history of quantum gravity, presented at the 9th Marcel Grossmann Meeting in Rome, July 2000. Available as gr-qc/0006061.

week161

1. Dava Sobel, Galileo's Daughter, Penguin Books, London, 2000.

2. David B. Wilson, Kelvin and Stokes: A Comparative Study in Victorian Physics, Adam Hilger, Bristol, 1987.

3. Don Howard and John Stachel eds., Einstein and the History of General Relativity, Birkhauser, Boston, 1989.

4. John Baez, The end of the universe, http://math.ucr.edu/home/baez/end.html

5. John D. Barrow and Frank J. Tipler, The Cosmological Anthropic Principle, Oxford U. Press, Oxford, 1988.

6. John D. Barrow, The Book of Nothing, to be published.

7. Bert Schroer, Facts and fictions about Anti de Sitter spacetimes with local quantum matter, available as hep-th/9911100.

8. Bert Schroer, Braided structure in 4-dimensional conformal quantum field theory, available as hep-th/0012021.

week162

1. The Universe Map, National Geographic Society, NSG #602011, 2000.

2. Wil Tirion and Roger W. Sinnot, Sky Atlas 2000.0, 2nd edition, Cambridge U. Press, 1999.

3. Lee Smolin, Three Roads to Quantum Gravity, Weidenfeld and Nicholson, 2000.

4. Lynn E. Garner, An Outline of Projective Geometry, North Holland, New York, 1981.

5. Ruth Moufang, Alternativkoerper und der Satz vom vollstaendigen Vierseit, Abhandlungen Math. Sem. Hamburg 9, (1933), 207-222.

6. Pascual Jordan, Ueber eine Klasse nichtassociativer hyperkomplexer Algebren, Nachr. Ges. Wiss. Goettingen (1932), 569-575.

7. Pascual Jordan, John von Neumann, Eugene Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. Math. 35 (1934), 29-64.

8. G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley-Interscience, New York, 1972.

9. Pascual Jordan, Ueber eine nicht-desarguessche ebene projektive Geometrie, Abhandlungen Math. Sem. Hamburg 16 (1949), 74-76.

10. Murat Gunaydin and Feza Gursey, An octonionic representation of the Poincare group, Lett. Nuovo Cim. 6 (1973), 401-406.

11. Murat Gunaydin and Feza Gursey, Quark structure and octonions, Jour. Math. Phys. 14 (1973), 1615-1667.

12. Murat Gunaydin and Feza Gursey, Quark statistics and octonions, Phys. Rev. D9 (1974), 3387-3391.

13. Murat Gunaydin, Octonionic Hilbert spaces, the Poincare group and SU(3), Jour. Math. Phys. 17 (1976), 1875-1883.

14. M. Gunaydin, C. Piron and H. Ruegg, Moufang plane and octonionic quantum mechanics, Comm. Math. Phys. 61 (1978), 69-85.

15. E. Corrigan and T. J. Hollowood, The exceptional Jordan algebra and the superstring, Commun. Math. Phys., 122 (1989), 393.

16. E. Corrigan and T. J. Hollowood, A string construction of a commutative nonassociative algebra related to the exceptional Jordan algebra, Phys. Lett. B203 (1988), 47.

17. G. Sierra, An application of the theories of Jordan algebras and Freudenthal triple systems to particles and strings, Class. Quant. Grav. 4 (1987), 227.

18. Corinne A. Manogue and Tevian Dray, Octonionic Moebius transformations, Mod. Phys. Lett. A14 (1999) 1243-1256, available as math-ph/9905024.

19. Anthony Sudbery, Division algebras, (pseudo)orthogonal groups and spinors, Jour. Phys. A17 (1984), 939-955.

20. Hans Freudenthal, Zur ebenen Oktavengeometrie, Indag. Math. 15 (1953), 195-200.

    Hans Freudenthal, Beziehungen der e₇ und e₈ zur Oktavenebene:

    I, II, Indag. Math. 16 (1954), 218-230, 363-368.

    III, IV, Indag. Math. 17 (1955), 151-157, 277-285.

    V - IX, Indag. Math. 21 (1959), 165-201, 447-474.

    X, XI, Indag. Math. 25 (1963) 453-471, 472-487.

    Hans Freudenthal, Lie groups in the foundations of geometry, Adv. Math. 1 (1964), 145-190.

    Hans Freudenthal, Oktaven, Ausnahmegruppen und Oktavengeometrie, Geom. Dedicata 19 (1985), 7-63.

21. Jacques Tits, Le plan projectif des octaves et les groupes de Lie exceptionnels, Bull. Acad. Roy. Belg. Sci. 39 (1953), 309-329.

    Jacques Tits, Le plan projectif des octaves et les groupes exceptionnels E₆ et E₇, Bull. Acad. Roy. Belg. Sci. 40 (1954), 29-40.

22. Tonny A. Springer, The projective octave plane, I-II, Proc. Koninkl. Akad. Wetenschap. A63 (1960), 74-101.

    Tonny A. Springer, On the geometric algebra of the octave planes, I-III, Proc. Koninkl. Akad. Wetenschap. A65 (1962), 413-451.

23. J. R. Faulkner and J. C. Ferrar, Exceptional Lie algebras and related algebraic and geometric structures, Bull. London Math. Soc. 9 (1977), 1-35.

24. Kevin McCrimmon, Jordan algebras and their applications, AMS Bulletin 84 (1978), 612-627.

week163

1. Georges Ifrah, The Universal History of Numbers from Prehistory to the Invention of the Computer, Wiley, New York, 2000.

2. Frequently asked questions about the MathWorld case, http://mathworld.wolfram.com/docs/faq.html

3. Gordon and Breach et al v. AIP and APS, brief of amici curiae of the American Library Association, Association of Research Libraries and the Special Library Association, http://www.arl.org/scomm/gb/amici.html

4. AIP/APS prevail in suit by Gordon and Breach, G&B to appeal, http://www.arl.org/newsltr/194/gb.html

5. John Stilwell, The story of the 120-cell, AMS Notices 48 (January 2001), 17-24.

6. Plato, Timaeus, translated by B. Jowett, in The Collected Dialogues, Princeton U. Press, Princeton, 1969 (see line 55c).

7. F. Reese Harvey, Spinors and Calibrations, Academic Press, Boston, 1990.

week164

1. Physics problems for the next millennium, http://feynman.physics.lsa.umich.edu/strings2000/millennium.html

2. What questions have disappeared?, The World Question Center, http://www.edge.org/documents/questions/q2001.html

3. Nobuo Shimada, Differentiable structures on the 15-sphere and Pontrjagin classes of certain manifolds, Nagoya Math. Jour. (12) 1957, 59-69.

4. Jack Morava, Cobordism of symplectic manifolds and asymptotic expansions, a talk at the conference in honor of S.P. Novikov's 60th birthday, available as math.SG/9908070.

5. Detlev Buchholz, Current trends in axiomatic quantum field theory, available as hep-th/9811233.

6. Matt Visser, The reliability horizon, available as gr-qc/9710020.

7. Bianca Letizia Cerchiai and Julius Wess, q-Deformed Minkowski Space based on a q-Lorentz Algebra, available as math.QA/9801104.

week165

1. University of Wisconsin at Milwaukee, Center for Gravitation and Cosmology home page, http://www.gravity.phys.uwm.edu/

2. Marcia Bartusiak, Einstein's Unfinished Symphony: Listening to the Sounds of Space-Time, Joseph Henry Press, Washington D.C., 2000.

3. J. Friedman and R. Sorkin, Spin 1/2 from gravity, Phys. Rev. Lett 44 (1980), 1100.

4. John Baez, The meaning of Einstein's equation, available at gr-qc/0103044.

5. John Baez, Toby Bartels and Miguel Carrion, Quantum Gravity Seminar, http://math.ucr.edu/home/baez/qg.html

6. Craig Callender and Nick Huggett, eds., Physics Meets Philosophy at the Planck Scale: Contemporary Theories in Quantum Gravity, Cambridge U. Press, Cambridge, 2001.

7. Martin Bojowald, Loop Quantum Cosmology I: Kinematics, Class. Quant. Grav. 17 (2000), 1489-1508, also available at gr-qc/9919103

   Loop Quantum Cosmology II: Volume Operators, Class. Quant. Grav. 17 (2000), 1509-1526, also available at gr-qc/9910104.

   Loop Quantum Cosmology III: Wheeler-DeWitt Operators, Class. Quant. Grav. 18 (2001), 1055-1070, also available at gr-qc/0008052.

   Loop Quantum Cosmology IV: Discrete Time Evolution, Class. Quant. Grav. 18 (2001) 1071-1088, also available at gr-qc/0008053.

   Absence of Singularity in Loop Quantum Cosmology, available at gr-qc/0102069.

8. Tom Leinster, General operads and multicategories, available as math.CT/9810053.

   Structures in higher-dimensional category theory, Ph.D. thesis, available at http://www.dpmms.cam.ac.uk/~leinster/shdctabs.html

   Up-to-homotopy monoids, available as math.QA/9912084.

   Homotopy algebras for operads, available as math.QA/0002180. math.QA/0002180.

   Operads in higher-dimensional category theory, available as math.CT/0011106

9. Eugenia Cheng, The relationship between the opetopic and multitopic approaches to weak n-categories, available at http://www.dpmms.cam.ac.uk/~elgc2/

   Equivalence between approaches to the theory of opetopes, available at http://www.dpmms.cam.ac.uk/~elgc2/

10. Hermann Nicolai and Robert Helling, Supermembranes and M(atrix) theory, available as hep-th/9809103.

11. Washington Taylor, M(atrix) theory: matrix quantum mechanics as a fundamental theory, available as hep-th/0101126.

week166

1. Steven Finch, MathSoft Constants, http://pauillac.inria.fr/algo/bsolve/constant/constant.html

2. The Mathematics Geneaology Project, http://hcoonce.math.mankato.msus.edu/

3. John J. O'Connor and Edmund F. Robertson, The MacTutor History of Mathematics Archive, http://www-groups.dcs.st-andrews.ac.uk/~history/index.html

4. Bernard Greenberg, The Mercator Projection, http://www.beanpaste.com/BSG/mercator.html

5. Anthony M. Jacobi, Academic Family Tree, http://www.staff.uiuc.edu/%7Ea-jacobi/tree.html

6. Robert L. Griess, Pieces of eight: semiselfdual lattices and a new foundation for the theory of Conway and Mathieu groups. Adv. Math. 148 (1999), 75-104.

7. John H. Conway, Christopher S. Simons, 26 implies the Bimonster, Jour. Algebra 235 (2001), 805-814.

8. Pierre Ramond, Boson-fermion confusion: the string path to supersymmetry, available at hep-th/0102012.

9. T. Pengpan and Pierre Ramond, M(ysterious) patterns in SO(9), Phys. Rep. 315 (1999) 137-152, also available as hep-th/9808190.

week167

1. Y. Jack Ng and H. van Dam, Measuring the foaminess of space-time with gravity-wave interferometers, Found. Phys. 30 (2000) 795-805, also available as gr-qc/9906003

2. Eugene P. Wigner, Relativistic invariance and quantum phenomena, Rev. Mod. Phys. 29 (1957), 255-268.

   H. Salecker and E. P. Wigner, Quantum limitations of the measurement of space-time distances, Phys. Rev. 109, (1958), 571-577. Also available at http://fangio.magnet.fsu.edu/~vlad/pr100/100yrs/html/chap14_toc.htm

3. Ronald J. Adler, Ilya M. Nemenman, James M. Overduin, David I. Santiago, On the detectability of quantum spacetime foam with gravitational-wave interferometers, Phys. Lett. B477 (2000) 424-428, also available at gr-qc/9909017.

4. Y. Jack Ng and H. van Dam, On Wigner's clock and the detectability of spacetime foam with gravitational-wave interferometers, Phys. Lett. B477 (2000) 429-435, also available at gr-qc/9911054.

5. G. Amelino-Camelia, Quantum theory's last challenge, Nature 408 (2000) 661-664.

   Testable scenario for relativity with minimum length, available at hep-th/0012238

6. Ronald J. Adler and David I. Santiago, On gravity and the uncertainty principle, Mod. Phys. Lett. A14 (1999) 1371, also available at gr-qc/9904026.

7. J. Ellis, N.E. Mavromatos and D. V. Nanopoulos, Search for quantum gravity, Gen. Rel. Grav. 31 (1999) 1257-1262, also available as gr-qc/9905048.

8. Jorge Pullin and Rodolfo Gambini, Nonstandard optics from quantum spacetime, Phys. Rev. D59 (1999) 124021, also available as gr-qc/9809038.

9. J. Ellis, K. Farakos, N.E. Mavromatos, V. Mitsou and D.V. Nanopoulos, Astrophysical probes of the constancy of the velocity of light, Astrophys. J. 535 (2000) 139-151, also available as astro-ph/9907340.

week168

1. Martin Bojowald, Quantum Geometry and Symmetry, Shaker Verlag, Aachen, 2000. Available at http://www.shaker.de/Online-Gesamtkatalog/Details.asp?ISBN=3-8265-7741-8

2. Martin Bojowald, The semiclassical limit of loop quantum cosmology, available at gr-qc/0105113.

3. Alejandro Perez, Finiteness of a spin foam model for euclidean quantum general relativity, Nucl. Phys. B599 (2001) 427-434. Also available at gr-qc/0011058.

4. John Baez and John W. Barrett, Integrability for relativistic spin networks, available at gr-qc/0101107.

5. Louis Crane, Alejandro Perez, Carlo Rovelli, A finiteness proof for the Lorentzian state sum spin foam model for quantum general relativity, available as gr-qc/0104057.

6. John Baez, The octonions, http://math.ucr.edu/home/baez/Octonions/octonions.html
   Also available at math.RA/0105155.

week169

1. Daniele Oriti, Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity, Rep. Prog. Phys. 64 (2001), 1489-1544. Also available at gr-qc/0106091.

2. Tom Leinster, Topology and higher-dimensional category theory: the rough idea, available at math.CT/0106240.

3. Markus Rost, On the dimension of a composition algebra, Documenta Mathematica 1 (1996), 209-214. Available at http://www.mathematik.uni-bielefeld.de/DMV-J/vol-01/10.html

4. Dominik Boos, Ein tensorkategorieller Zugang zum Satz von Hurwitz (A tensor-categorical approach to Hurwitz's theorem), Diplomarbeit ETH Zurich, March 1998, available at http://www.math.ohio-state.edu/~rost/tensors.html

5. John Baez, Topos theory in a nutshell, http://math.ucr.edu/home/baez/topos.html

6. John Baez, Toby Bartels, and Miguel Carrion, Quantum gravity seminar, http://math.ucr.edu/home/baez/qg.html

week170

1. Conference on Algebraic Topological Methods in Computer Science, Stanford University, http://math.stanford.edu/atmcs/index.htm

2. Alejandro Perez, Finiteness of a spin foam model for euclidean quantum general relativity, Nucl. Phys. B599 (2001) 427-434. gr-qc/0011058.

3. John W. Barrett, The classical evaluation of relativistic spin networks, Adv. Theor. Math. Phys. 2 (1998), 593-600. Also available as math.QA/9803063.

4. John W. Barrett and Ruth M. Williams, The asymptotics of an amplitude for the 4-simplex, Adv. Theor. Math. Phys. 3 (1999), 209-215. Also available as gr-qc/9809032.

5. Noson S. Yanofsky, Obstructions to coherence: natural noncoherent associativity, Jour. Pure Appl. Alg. 147 (2000), 175-213. Also available at math.QA/9804106.

   The syntax of coherence. To appear in Cahiers Top. Geom. Diff.. Also available at math.CT/9910006.

   Coherence, homotopy and 2-theories. To appear in K-Theory. Also available at math.CT/0007033.

6. G. Maxwell Kelly and Ross Street, Review of the elements of 2-categories, Springer Lecture Notes in Mathematics 420, Berlin, 1974, pp. 75-103.

7. Daniel G. Quillen, Homotopical Algebra, Springer Lecture Notes in Mathematics, vol. 43, Springer, Berlin, 1967.

8. Mark Hovey, Model Categories, American Mathematical Society Mathematical Surveys and Monographs, vol 63., Providence, Rhode Island, 1999.

9. Paul G. Goerss and John F. Jardine, Simplicial Homotopy Theory, Birkhauser, Boston, 1999.

week171

1. Urban legends reference pages, The Prize's Rite, http://www.snopes2.com/science/nobel.htm

2. Steve Carlip, Quantum gravity: a progress report, Rep. Prog. Phys. 64 (2001) 885-942, also available at gr-qc/0108040.

3. Ulf Daniellson, Introduction to string theory, Rep. Prog. Phys. 64 (2001) 51-96.

4. Thomas Thiemann, Introduction to modern canonical quantum general relativity, 301 pages, available at gr-qc/0110034.

5. Rodolfo Gambini and Jorge Pullin, Consistent discretizations for classical and quantum general relativity, available as gr-qc/0108062.

6. Luca Bombelli, Statistical geometry of random weave states, available as gr-qc/0101080.

7. Michael Seifert, Angle and volume studies in quantized space, 85 pages, available as gr-qc/0108047.

   Paul Chew, Voronoi/Delaunay Applet, http://www.cs.cornell.edu/Info/People/chew/Delaunay.html

week172

1. Discrete Random Geometries and Quantum Gravity, http://www1.phys.uu.nl/Symposion/EUWorkshop.htm

2. Wil McCarthy, Ultimate alchemy, Wired, October 2001, 150.

3. Marc Kastner, Artificial atoms, Physics Today 46 (1993), 24. Also available at http://web.mit.edu/physics/people/marc_kastner.htm

4. Leo Kouwenhoven and Charles Marcus, Quantum dots, Physics World, June 1998. Also available at http://marcuslab.harvard.edu/

5. Terry Gannon, Monstrous moonshine and the classification of CFT, in Conformal Field Theory: New Non-Perturbative Methods in String and Field Theory, Yavuz Nutku, Cihan Saclioglu and Teoman Turgut, eds., Perseus Publishing, 2000.

6. Sergeui N. Dorogovtsev and J.F.F. Mendes, Evolving networks, available at cond-mat/0106144.

7. John Baez and J. Daniel Christensen, Positivity of spin foam amplitudes, available at gr-qc/0110044.

8. J. Daniel Christensen and Greg Egan, An efficient algorithm for the Riemannian 10j symbols, available at gr-qc/0110045.

9. N. Ishibashi, H. Kawai, Y. Kitazawa and T. Tsuchiya, A large-N reduced model as superstring, Nucl. Phys. B498 (1997) 467-491. Also available as hep-th/9612115.

10. Peter Austing and John F. Wheater, Convergent Yang-Mills matrix theories, JHEP 0104 (2001) 019. Also available as hep-th/0103159.

11. Z. Burda, B. Petersson, J. Tabaczek, Geometry of reduced supersymmetric 4D Yang-Mills integrals, Nucl. Phys. B602 (2001) 399-409. Also available as hep-lat/0012001.

12. A. Konechny and A. Schwarz, Introduction to M(atrix) theory and noncommutative geometry, available at hep-th/0012145.

13. A. J. Wilkie, On exponentiation - a solution to Tarski's high school algebra problem, to appear in Quaderni di Matematica. Also available at http://www.maths.ox.ac.uk/~wilkie/

14. R. Gurevic, Equational theory of positive numbers with exponentiation, Proc. Amer. Math. Soc. 94 (1985), 135-141.

15. Marcel G. Jackson, A note on HSI-algebras and counterexamples to Wilkie's identity, Algebra Universalis 36 (1996), 528-535. Also available at http://www.latrobe.edu.au/mathstats/Staff/Marcel/details/publications.html

16. R. Gurevic, Equational theory of positive numbers with exponentiation is not finitely axiomatizable, Ann. Pure. Appl. Logic 49 (1990), 1-30.

week173

1. Favorite Leonid images found posted on the net, http://leonids.arc.nasa.gov/image_favorites.html

2. Thomas Püttmann and A. Rigas, Isometric actions on the projective planes and embedded generators of homotopy groups. Available at http://www.ruhr-uni-bochum.de/mathematik8/puttmann/index.html.

3. Matteo Mainetti and Catherine Huafei Yan, Arguesian identities in linear lattices, Adv. Math. 144 (1999), 50-93.

4. Mark Haiman, Proof theory for linear lattices, Adv. Math. 58 (1985), 209-242.

5. D. Finberg, M. Mainetti and G.-C. Rota, The logic of commuting equivalence relations, in Logic and Algebra, eds. A. Ursini and P. Agliano, Lecture Notes in Pure and Applied Mathematics, vol. 180, Decker, New York 1996.

6. Michael Mueger, Conformal field theory and Doplicher-Roberts reconstruction, available at math-ph/0008027.

   From subfactors to categories and topology I: Frobenius algebras in and Morita equivalence of tensor categories, available at math.CT/0111204.

   From subfactors to categories and topology II: The quantum double of tensor catgories and subfactors, available at math.CT/0111205.

week174

1. Thomas Hawkins, The Emergence of the Theory of Lie Groups: an Essay in the History of Mathematics, 1869-1926, Springer, New York, 2000.

2. Michael Mueger, From subfactors to categories and topology I: Frobenius algebras in and Morita equivalence of tensor categories, available at math.CT/0111204.

3. Stephen Schanuel and Ross Street, The free adjunction, Cah. Top. Geom. Diff. 27 (1986), 81-83.

4. Frank Quinn, Lectures on axiomatic quantum field theory, in Geometry and Quantum Field Theory, Amer. Math. Soc., Providence, RI, 1995.

5. Lowell Abrams, Two-dimensional topological quantum field theories and Frobenius algebras, J. Knot Theory and its Ramifications 5 (1996), 569-587.

6. L. Kadison, New Examples of Frobenius Extensions, University Lecture Series #14, Amer. Math. Soc., Providence RI, 1999.

week175

1. Dava Sobel, Longitude, Fourth Estate Ltd., London, 1996.

2. E. G. Richards, Mapping Time: The Calendar and its History, Oxford U. Press, Oxford, 1998.

3. John Baez, The wobbling of the earth and other curiosities, http://math.ucr.edu/home/baez/wobble.html

4. Alain Connes, Andre Lichnerowicz and Marcel Paul Schutzenberger, A Triangle of Thoughts, AMS, Providence, 2000.

5. Masamichi Takesaki, Theory of Operator Algebras I, Springer, Berlin, 1979.

6. Richard V. Kadison and John Ringrose, Fundamentals of the Theory of Operator Algebras, 4 volumes, Academic Press, New York, 1983-1992.

7. Shoichiro Sakai, C*-algebras and W*-algebras, Springer, Berlin, 1971.

8. Gerard G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, Wiley-Interscience, New York, 1972.

9. Rudolf Haag, Local Quantum Physics: Fields, Particles, Algebras, Springer, Berlin, 1992.

10. Ola Bratelli and Derek W. Robinson, Operator Algebras and Quantum Statistical Mechanics, 2 volumes, Springer, Berlin, 1987-1997.

week176

1. Jan T. Kleyna, Mark I. Wilkinson, N. Wyn Evans and Gerard Gilmore, First clear signature of an extended dark matter halo in the Draco dwarf spheroidal, Astrophysical Journal Letters 563 (2001), L115-118. Also available at astro-ph/0111329.

2. UK Dark Matter Collaboration (UKDMC) homepage, http://hepwww.rl.ac.uk//UKDMC/

3. DAMA collaboration, Searching for the WIMP annual signature by the ~100 kg NaI(Tl) set-up, http://www.lngs.infn.it/lngs/htexts/dama/dama39.html

4. Dark Matter (DAMA) experiment home page, http://www.lngs.infn.it/lngs/htexts/dama/welcome.html

5. Cryogenic Dark Matter Search (CDMS) home page, http://cdms.berkeley.edu/

6. Frederic Mayet, Dark Matter Portal, http://isnwww.in2p3.fr/ams/fred/dm.html

7. Edward R. Harrison, Cosmology, the Science of the Universe, Cambridge University Press, Cambridge, 1981.

8. M. Berry, Cosmology and Gravitation, Adam Hilger, Bristol, 1986.

9. John A. Peacock, Cosmological Physics, Cambridge University Press, Cambridge, 1999.

10. Shaaban Khalil and Carlos Munoz, The enigma of the dark matter, to appear in Contemp. Phys., also available at hep-ph/0110122.

11. Leszek Roszkowski, Non-baryonic dark matter, available as hep-ph/0102327.

12. B. J. Carr, Recent developments in the search for baryonic dark matter, available as astro-ph/0102389.

13. V. C. de Andrade, L. C. T. Guillen and J. G. Pereira, Teleparallel gravity: an overview, available at gr-qc/0011087.

14. Yakov Itin, Energy-momentum current for coframe gravity, available as gr-qc/0111036.

15. From subfactors to categories and topology I: Frobenius algebras in and Morita equivalence of tensor categories, available as math.CT/0111204.

16. Michael Mueger, On the structure of modular categories, available as math.CT/0201017.

week177

1. Greg Egan, Schild's Ladder, Eos, May 2002. Synopsis available at http://www.netspace.net.au/~gregegan/SCHILD/SCHILD.html

2. Abhay Ashtekar, Quantum geometry and gravity: recent advances, available as gr-qc/0112038.

   Abhay Ashtekar, Quantum geometry in action: big bang and black holes, available as math-ph/0202008.

3. Aleksandar Mikovic, Spin foam models of matter coupled to gravity, hep-th/0108099.

   Aleksandar Mikovic, Quantum field theory of open spin networks and new spin foam models, available as gr-qc/0202026.

4. Matthias Arnsdorf, Relating covariant and canonical approaches to triangulated models of quantum gravity, available as gr-qc/0110026.

5. Rodolfo Gambini and Jorge Pullin, A finite spin-foam-based theory of three and four dimensional quantum gravity, gr-qc/0111089.

6. Robert Oeckl, Generalized lattice gauge theory, spin foams and state sum invariants, available as hep-th/0110259.

   Florian Girelli, Robert Oeckl and Alejandro Perez, Spin foam diagrammatics and topological invariance, available as gr-qc/0111022.

7. John C. Baez, J. Daniel Christensen, Thomas R. Halford and David C. Tsang, Spin foam models of Riemannian quantum gravity, gr-qc/0202017.

8. Roberto De Pietri, Laurent Freidel, Kirill Krasnov, and Carlo Rovelli, Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space, preprint available as hep-th/9907154.

9. Alejandro Perez and Carlo Rovelli, A spin foam model without bubble divergences, Nucl. Phys. B599 (2001), 255-282. Also available as gr-qc/0006107.

   Alejandro Perez, Finiteness of a spin foam model for Euclidean quantum general relativity, Nucl. Phys. B599 (2001), 427-434. Also available as gr-qc/0011058.

   Alejandro Perez, Group quantum field theories and spin foam models for quantum gravity, to appear.

week178

1. J. Peter May, Operadic categories, A_infinity categories and n-categories, writeup of a talk given in Morelia, Mexico, May 25, 2001. Available with other papers at his homepage, http://www.math.uchicago.edu/~may/

2. Tom Leinster, A survey of definitions of n-category, available at math.CT/0107188.

3. Carlos Simpson, Some properties of the theory of n-categories, available at math.CT/0110273. math.CT/0110273.

4. Martin Markl, Steve Shnider and Jim Stasheff, Operads in Algebra, Topology and Physics, AMS, Providence, 2002.

5. F. Morel, Voevodsky's proof of Milnor's conjecture, Bull. Amer. Math. Soc. 35 (1998), 123-143. Also available at http://e-math.ams.org/jourcgi/amsjournal?fn=120&pg1=pii&s1=S0273097998007459

6. Hans Freudenthal, Lie groups in the foundations of geometry, Adv. Math. 1 (1964), 145-190.

7. Hans Freudenthal and H. de Vries, Linear Lie groups, Academic Press, New York, 1969.

8. William Fulton and Joe Harris, Representation Theory - a First Course, Springer Verlag, Berlin, 1991.

9. Robert J. Baston and Michael G. Eastwood, The Penrose Transform: its Interaction with Representation Theory, Clarendon Press, Oxford,

week179

1. Alain Connes and Dirk Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and main theorem, Comm. Math. Phys. 210 (2000), 249-273. Also available as hep-th/9912092.

2. G. Scharf, Finite Quantum Electrodynamics, Springer, Berlin, 1995.

3. Alain Connes and Dirk Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem I: the beta-function, diffeomorphisms and the renormalization group, Comm. Math. Phys. 216 (2001), 215-241. Also available as hep-th/0003188.

4. Dirk Kreimer, Knots and Feynman Diagrams, Cambridge University Press, Cambridge, 2000.

5. Andrew Pressley and Graeme Segal, Loop Groups, Oxford University Press, Oxford, 1986.

6. David Berenstein, Juan Maldacena and Horatiu Nastase, Strings in flat space and pp waves from N = 4 Super Yang Mills, available as hep-th/0202021.

7. Yuri Manin and Matilde Marcolli, Holography principle and arithmetic of algebraic curves, available as hep-th/0201036.

week180

1. Cosmic X-rays reveal evidence for new form of matter, http://www1.msfc.nasa.gov/NEWSROOM/news/releases/2002/02-082.html

2. Peter Johnstone, Sketches of an Elephant: a Topos Theory Compendium, Cambridge U. Press. Volume 1, comprising Part A: Toposes as Categories, and Part B: 2-categorical Aspects of Topos Theory, 720 pages, to appear in June 2002. Volume 2, comprising Part C: Toposes as Spaces, and Part D: Toposes as Theories, 880 pages, to appear in June 2002. Volume 3, comprising Part E: Homotopy and Cohomology, and Part F: Toposes as Mathematical Universes, in preparation.

3. John Baez, Topos theory in a nutshell, http://math.ucr.edu/home/baez/topos.html

4. Colin McLarty, Elementary Categories, Elementary Toposes, Oxford University Press, Oxford, 1992.

5. William Fulton and Joe Harris, Representation Theory - a First Course, Springer Verlag, Berlin, 1991.

6. Robert J. Baston and Michael G. Eastwood, The Penrose Transform: its Interaction with Representation Theory, Clarendon Press, Oxford, 1989.

7. S. A. Huggett and K.P. Tod, An Introduction to Twistor Theory, Cambridge U. Press, Cambridge, 1994.

week181

1. Alain Chenciner and Richard Montgomery, A remarkable periodic solution of the three-body problem in the case of equal masses, Ann. of Math. 152 (2000), 881-901. Also available as math.DS/0011268.

2. Richard Montgomery, A new solution to the three-body problem, AMS Notices 48 (May 2001), 471-481. Also available as http://www.ams.org/notices/200105/fea-montgomery.pdf

3. Bill Casselman, A new solution to the three body problem - and more, at http://www.ams.org/new-in-math/cover/orbits1.html

4. Christopher Moore, Braids in classical gravity, Phys. Rev. Lett. 70 (1993), 3675-3679.

5. Richard Montgomery, The N-body problem, the braid group, and action-minimizing periodic solutions, Nonlinearity 11 (1998), 363-371.

6. Zhihong Xia, The existence of non-collision singularities in Newtonian systems, Ann. Math. 135 (1992), 411-468.

7. Donald G. Saari and Zhihong Xia, Off to infinity in finite time, AMS Notices (May 1995), 538-546. Also available at http://www.ams.org/notices/199505/saari-2.pdf

8. John Baez, Geometric quantization, http://math.ucr.edu/home/baez/quantization.html

9. J. Snyatycki, Geometric Quantization and Quantum Mechanics, Springer-Verlag, New York, 1980.

10. Nicholas Woodhouse, Geometric Quantization, Oxford U. Press, Oxford, 1992.

11. Norman E. Hurt, Geometric Quantization in Action: Applications of Harmonic Analysis in Quantum Statistical Mechanics and Quantum Field Theory, Kluwer, Boston, 1983.

week182

1. David Eppstein, Egyptian fractions, http://www.ics.uci.edu/~eppstein/numth/egypt/

2. Alan Swett, The Erdos-Strauss conjecture, http://math.uindy.edu/swett/esc.htm

3. H. S. M. Coxeter, Generators and relations for discrete groups, Springer, Berlin, 1984.

4. Joris van Hoboken, Platonic solids, binary polyhedral groups, Kleinian singularities and Lie algebras of type A,D,E, Master's Thesis, University of Amsterdam, 2002, available at http://www.science.uva.nl/research/math/examen/2002/scriptiejoris.ps

5. MSRI streaming video archive, Spring 2002, http://www.msri.org/publications/video/index04.html

6. R. O. Wells, Differential analysis on complex manifolds, Springer, Berlin, 1980.

7. Tony Pantev, Review of abelian Hodge theory, http://www.msri.org/publications/ln/msri/2002/introstacks/pantev/1/index.html

8. Ludmil Katzarkov, Tony Pantev and Bertrand Toen, Schematic homotopy types and non-abelian Hodge theory I: The Hodge decomposition, available at math.AG/0107129.

9. Bertrand Toen, Toward a Galoisian interpretation of homotopy theory, 9vailable as math.AT/0007157.

10. Bertrand Toen and Gabriele Vezzosi, Algebraic geometry over model categories (a general approach to derived algebraic geometry), available as math.AG/0110109.

week183

1. Victor Kac and Pokman Cheung, Quantum Calculus, Springer, Berlin, 2002.

2. George E. Andrews, Richard Askey, Ranjan Roy, Special Functions, Cambridge U. Press, Cambridge, 1999.

3. Shahn Majid, Foundations of Quantum Group Theory, Cambridge U. Press, Cambridge, 2000.

4. John Barrett, Geometrical measurements in three-dimensional quantum gravity, available as gr-qc/0203018.

week184

1. I. M. James, editor, History of Topology, Elsevier, New York, 1999.

2. Andrew Pressley and Graeme Segal, Loop Groups, Oxford U. Press, Oxford, 1986.

3. Vyjayanathi Chari and Andrew Pressley, A Guide to Quantum Groups, Cambridge U. Press, Cambridge, 1994.

4. Juergen Fuchs, Affine Lie Algebras and Quantum Groups, Cambridge U. Press, Cambridge, 1992.

week185

1. Yu. I. Manin, Quantum Groups and Noncommutative Geometry, Les Publ. du Centre de Recherches Math., Universite de Montreal, Montreal, 1988.

2. John Baez and Michael Weiss, Photons, schmotons, available at http://math.ucr.edu/home/baez/photon

3. John Baez and James Dolan, From finite sets to Feynman diagrams, in Mathematics Unlimited - 2001 and Beyond, vol. 1, eds. Bjorn Engquist and Wilfried Schmid, Springer, Berlin, 2001, pp. 29-50. Also available as math.QA/0004133.

4. Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, Concrete Mathematics: a Foundation for Computer Science, 2nd edition, Addison-Wesley, Reading, Massachusetts, 1994.

5. Herbert Wilf, Generatingfunctionology, Academic Press, Boston, 1994. Also available for free at http://www.cis.upenn.edu/~wilf/

6. Richard P. Stanley, Enumerative Combinatorics, two volumes, Cambridge U. Press, Cambridge, 1999.

7. Andre Joyal, Une theorie combinatoire des series formelles, Adv. Math. 42 (1981), 1-82.

8. Andre Joyal, Foncteurs analytiques et especes de structures, in Combinatoire Enumerative, Springer Lecture Notes in Mathematics 1234, Springer, Berlin (1986), 126-159.

9. F. Bergeron, G. Labelle, and P. Leroux, Combinatorial species and tree-like structures, Cambridge, Cambridge U. Press, 1998.

10. Andre Joyal and Ross Street, The category of representations of the general linear groups over a finite field, Jour. Alg. 176 (1995), 908-945.

week186

1. William Fulton and Joe Harris, Representation Theory - a First Course, Springer Verlag, Berlin, 1991.

2. Francois Digne and Jean Michel, Representations of Finite Groups of Lie Type, London Mathematical Society Student Texts 21, Cambridge U. Press, Cambridge, 1991.

3. Kenneth S. Brown, Buildings, Springer, Berlin, 1989.

4. Paul Garrett, Buildings and Classical Groups, Chapman & Hall, London, 1997.

5. Antonio Pasini, Diagram Geometries, Oxford U. Press, Oxford, 1994.

6. Jacques Tits, Buildings of Spherical Type and Finite BN-pairs, Springer Lecture Notes in Mathematics 386, Berlin, New York, 1974.

week187

1. Robin Hartshorne, Algebraic Geometry, Appendix C: The Weil conjectures, Springer-Verlag, Berlin, 1977.

week188

1. A. W. F. Edwards, Pascal's Arithmetical Triangle, Charles Griffin and Co., London, 1987.

2. Jean Bellisard, K-theory of C*-algebras in solid state physics, in Lecture Notes in Physics vol. 237, Springer, Berlin, 1986, pp. 99-156.

3. Alain Connes, Noncommutative Geometry, Academic Press, New York, 1994.

4. Richard Szabo, Quantum field theory on noncommutative spaces, available as hep-th/0109162.

5. Marc Rieffel, Noncommutative tori: a case study of noncommutative differential manifolds, in Geometric and topological invariants of elliptic operators Contemp. Math. 105, American Mathematical Society, 1990, pp. 191-211.

week189

1. W. Wayt Gibbs, Ultimate clocks, Scientific American, September 2002, pp. 86-93.

2. Scott A. Diddams et al, An optical clock based on a single trapped Hg-199+ ion, Science, 293 (August 3 2001), 825-828.

3. Curt Cutler and Kip Thorne, An overview of gravitational-wave sources, available as gr-qc/0204090.

4. First lock at LIGO Hanford Observatory, http://www.ligo.caltech.edu/LIGO_web/firstlock/

5. Washington quake rattles Hanford Observatory, http://www.ligo.caltech.edu/LIGO_web/news/0228quake.html

6. LIGO's first science run: a special report, http://www.ligo.caltech.edu/LIGO_web/0209news/0209s1r1.html

7. Olaf Dreyer, Quasinormal modes, the area spectrum, and black hole entropy, gr-qc/0211076.

8. Stephen Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975), 199-220.

9. Abhay Ashtekar, John Baez, Alejandro Corichi and Kirill Krasnov, Quantum geometry and black hole entropy, Phys. Rev. Lett. 80 (1998) 904-907, also available at gr-qc/9710007.

10. Abhay Ashtekar, Alejandro Corichi and Kirill Krasnov, Isolated horizons: the classical phase space, Adv. Theor. Math. Phys. 3 (2000), 418-471, available as gr-qc/9905089.

    Abhay Ashtekar, John Baez and Kirill Krasnov, Quantum geometry of isolated horizons and black hole entropy, Adv. Theor. Math. Phys. 4 (2000), 1-94, available as gr-qc/0005126.

11. Hans-Peter Nollert, Quasinormal modes of Schwarzschild black holes: the determination of quasinormal frequencies with very large imaginary parts, Phys. Rev. D47 (1993), 5253-5258.

12. Nils Andersson, On the asymptotic distribution of quasinormal-mode frequencies for Schwarzschild black holes, Class. Quant. Grav. 10 (1993), L61-L67.

13. Hans-Peter Nollert, Quasinormal modes: the characteristic `sound' of black holes and neutron stars, Class. Quant. Grav. 16 (1999), R159-R216.

    K. D. Kokkotas and B. G. Schmidt, Quasi-normal modes of stars and black holes, Living Reviews in Relativity 2 (1999) 2, online at http://www.livingreviews.org/Articles/Volume2/1999-2kokkotas/; Also available at gr-qc/9909058.

14. Shahar Hod, Bohr's correspondence principle and the area spectrum of quantum black holes, Phys. Rev. Lett. 81 (1998), 4293-4296, also available as gr-qc/9812002.

15. Shahar Hod, Gravitation, the quantum, and Bohr's correspondence principle, Gen. Rel. Grav. 31 (1999) 1639, also available as gr-qc/0002002.

16. Jacob D. Bekenstein, Lett. Nuovo Cimento 11 (1974), 467.

    V. F. Mukhanov, Are black holes quantized?, JETP Lett. 44 (1986), 63-66.

    Jacob D. Bekenstein and V. F. Mukhanov, Spectroscopy of the quantum black hole, Phys. Lett B360 (1995), 7-12.

week190

1. Heinz-Juergen Schmidt, Structuralism in physics, The Stanford Encyclopedia of Philosophy (Winter 2002 Edition), ed. Edward N. Zalta, http://plato.stanford.edu/entries/physics-structuralism/

2. John Earman and Gordon Belot, Pre-Socratic quantum gravity, in Physics Meets Philosophy at the Planck Scale, eds. Chris Callender and Nick Huggett, Cambridge U. Press, Cambridge, 2001.

3. Aristidis Arageorgis, John Earman, and Laura Ruetsche, Weyling the time away: the non-unitary implementability of quantum field dynamics on curved spacetime, in Studies in the History and Philosophy of Modern Physics, in press.

4. Gordon Belot, John Earman and Laura Ruetsche, The Hawking information loss paradox: the anatomy of a controversy, British Journal for the Philosophy of Science, 50 (1999), 189-230.

5. G. Tanner, K. Richter and J. Rost, The theory of two-electron atoms: between ground state and complete fragmentation, Reviews of Modern Physics 72 (2000), 497-544.

6. J. Leopold and I. Percival, The semiclassical two-electron atom and the old quantum theory, Jour. Phys. B13 (1980) 1037-1047.

7. G. Ezra, K. Richter, G. Tanner, and D. Wintgen, Semiclassical cycle expansion for the helium atom, Journal of Physics B 24 (1991), L413-L420.

8. D. ter haar, The Old Quantum Theory, Pergamon Press, London, 1967.

9. Predrag Cvitanovic, Roberto Artuso, Per Dahlqvist, Ronnie Mainieri, Gregor Tanner, Gabor Vattay, Niall Whelan and Andreas Wirzba, Chaos: Classical and Quantum, http://www.nbi.dk/ChaosBook/

10. Predrag Cvitanovic, Group Theory, http://www.nbi.dk/GroupTheory/

11. Andreas Blass, Seven trees in one, Jour. Pure Appl. Alg. 103 (1995), 1-21. Also available at http://www.math.lsa.umich.edu/~ablass/cat.html

12. Marcelo Fiore and Tom Leinster, Objects of categories as complex numbers, available as math.CT/0212377.

week191

1. Antoine Van Proeyen, Structure of supergravity theories, available as hep-th/0301005.

2. Arjan Keurentjes, The group theory of oxidation, available as hep-th/0210178.

3. Luis J. Boya, Octonions and M-theory, available as hep-th/0301037.

4. Pierre Ramond, Exceptional groups and physics, available as hep-th/0301050.

5. Martin Markl, Steve Schnider and Jim Stasheff, Operads in Algebra, Topology and Physics, AMS, Providence, Rhode Island, 2002.

6. James Stasheff, Hartford/Luminy talks on operads, available at http://www.math.unc.edu/Faculty/jds/operadchik.ps.

7. Alexander Voronov, Notes on universal algebra, available as math.QA/0111009.

week192

1. Ruth Sime, Lise Meitner: A Life in Physics, University of California Press, 1997.

2. Argonne National Laboratory, Natural decay series, http://www.ead.anl.gov/pub/doc/NaturalDecaySeries.pdf

3. Emilio Segre, Enrico Fermi: Physicist, U. of Chicago Press, Chicago, 1970.

4. Abraham Pais, Niels Bohr's Times: in Physics, Philosophy and Polity, Oxford U. Press, Oxford, 1991.

5. The Neutron and the Bomb: a Biography of Sir James Chadwick, Oxford U. Press, Oxford, 1997.

6. Lise Meitner online, http://www.users.bigpond.com/Sinclair/fission/LiseMeitner.html

7. Lubos Motl, An analytical computation of asymptotic Schwarzschild quasinormal frequencies, available at gr-qc/0212096.

8. Alejandro Corichi, On quasinormal modes, black hole entropy, and quantum geometry, available at gr-qc/0212126.

9. Lubos Motl and Andrew Neitzke, Asymptotic black hole quasinormal frequencies, available at hep-th/0301173.

10. Shahar Hod, Kerr black hole quasinormal frequencies, available at gr-qc/0301122.

11. John Baez, The quantum of area?, Nature 421 (Feb. 13 2003), 702-703.

    John Baez, Quantization of area: the plot thickens, to appear in Spring 2003 edition of Matters of Gravity at http://www.phys.lsu.edu/mog/

    Both also available at http://math.ucr.edu/home/baez/area.html

12. Pascual Jordan, Ueber eine Klasse nichtassociativer hyperkomplexer Algebren, Nachr. Ges. Wiss. Goettingen (1932), 569-575.

13. C. M. Glennie, Some identities valid in special Jordan algebras but not in all Jordan algebras, Pacific J. Math. 16 (1966), 47-59.

14. Kevin McCrimmon, Zelmanov's prime theorem for quadratic Jordan algebras, Jour. Alg. 76 (1982), 297-326.

15. Murray Bremner, Using linear algebra to discover the defining identities for Lie and Jordan algebras, available at http://math.usask.ca/~bremner/research/colloquia/calgarynew.pdf

16. Murray Bremner, Quantum octonions, Communications in Algebra 27 (1999), 2809-2831, also available at http://math.usask.ca/~bremner/research/publications/qo.pdf

17. Georgia Benkart, Jose M. Pirez-Izquierdo, A quantum octonion algebra, Trans. Amer. Math. Soc. 352 (2000), 935-968, also available at math.QA/9801141.

week193

1. Murat Gunaydin, Koepsell and Hermann Nicolai, Conformal and quasiconformal realizations of exceptional Lie groups, Commun. Math. Phys. 221 (2001), 57-76, also available as hep-th/0008063

2. Thomas A. Larsson, Structures preserved by exceptional Lie algebras, available as math-ph/0301006.

3. Neil J. A. Sloane, Index of Lattices, the E8 lattice: coding version, http://www.research.att.com/~njas/lattices/E8_code.html

4. Kevin McCrimmon, Jordan Algebras and their applications, Bull. AMS 84 (1978) 612-627.

5. Kevin McCrimmon, A Taste of Jordan Algebras, Springer, Berlin, perhaps to appear in March 2003. Available for free online at http://math1.uibk.ac.at/mathematik/jordan/archive/atoja/ - but watch out, it's 545 pages long!

6. J. Tits, Une class d'algebres de Lie en relations avec les algebres de Jordan, Ned. Akad. Wet., Proc. Ser. A 65 (1962), 530.

7. M. Koecher, Imbedding of Jordan algebras into Lie algebra I, Am. J. Math. 89 (1967), 787.

8. Soji Kaneyuki, Graded Lie algebras, related geometric structures, and pseudo-hermitian symmetric spaces, in Analysis and Geometry on Complex Homogeneous Domains, by Faraut, Kaneyuki, Koranyi, Lu, and Roos, Birkhauser, New York, 2000.

9. Tony Smith, Graded Lie algebras, http://www.innerx.net/personal/tsmith/GLA.html

10. I. Kantor, I. Skopets, Some results on Freudenthal triple systems, Sel. Math. Sov. 2 (1982), 293.

11. K. Meyberg, Eine Theorie Der Freudenthalschen Tripelsysteme, I, II, Ned. Akad. Wet., Proc. Ser. A 71 (1968), 162-190.

12. R. Skip Garibaldi, Structurable algebras and groups of types E6 and E7, available at math.RA/9811035.

13. R. Skip Garibaldi, Groups of type E7 over arbitrary fields, available at math.RA/9811056.

14. G. Sierra, An application of the theories of Jordan algebras and Freudenthal triple systems to particles and strings, Class. Quant. Grav. 4 (1987), 227-236.

week194

1. John H. Conway and Derek A. Smith, On Quaternions and Octonions: Their Geometry, Arithmetic, and Symmetry, A. K. Peters, Ltd., Natick, Massachusetts, 2003.

2. Charles Seife, Mathemagician (impressions of Conway), The Sciences (May/June 1994), 12-15. Available at http://www.users.cloud9.net/~cgseife/conway.html

3. John H. Conway and Francis Fung, The Sensual (Quadratic) Form, Mathematical Association of America, Washington DC, 1997.

4. John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus, New York, 1996.

5. NIST, The 17 two-dimensional space groups, http://www.nist.gov/srd/webguide/nist42-3/appa.htm

6. Eric Weisstein, Wallpaper groups, http://mathworld.wolfram.com/WallpaperGroups.html

7. David Hestenes, Point groups and space groups in geometric algebra, modelingnts.la.asu.edu/pdf/crystalsymmetry.pdf

8. B. S. Acharya, M theory, G2 manifolds and four-dimensional physics, Class. Quant. Grav. 19 (2002), 5619-5653.

week195

1. Perimeter Institute, http://perimeterinstitute.ca/

2. Lee Smolin, How far are we from the quantum theory of gravity?, available as hep-th/0303185.

3. Eric D'Hoker and D.H. Phong, Lectures on two-loop superstrings, available as hep-th/0211111.

4. Eric D'Hoker and D.H. Phong, Two-loop superstrings: I, The main formulas, Phys. Lett. B529 (2002), 241-255. Also available as hep-th/0110247.

   II, The chiral measure on moduli space, Nucl. Phys. B636 (2002), 3-60. Also available as hep-th/0110283.

   III, Slice independence and absence of ambiguities, Nucl. Phys. B636 (2002), 61-79. Also available as hep-th/0111016.

   IV, The cosmological constant and modular forms, Nucl. Phys. B639 (2002), 129-181. Also available as hep-th/0111040.

5. Zvi Bern, Perturbative quantum gravity and its relation to gauge theory, Living Rev. Relativity 5 (2002), available at http://www.livingreviews.org/Articles/Volume5/2002-5bern/index.html

6. Stanley Deser, Nonrenormalizability of (last hope) D=11 supergravity, with a terse survey of divergences in quantum gravities, available as hep-th/9905017.

7. Stanley Deser, Infinities in quantum gravities, Annalen Phys. 9 (2000) 299-307. Also available as gr-qc/9911073.

week196

1. James B. Hartle, Gravity: an Introduction to Einstein's General Relativity, Addison-Wesley, San Francisco, 2003.

2. Dominik J. Schwarz, The first second of the universe, available as astro-ph/0303574.

3. Steven Weinberg, The First Three Minutes, Basic Books, New York, 1977.

4. Ned Wright's Cosmology Tutorial, http://www.astro.ucla.edu/~wright/cosmolog.htm

5. Martin White, The Cosmic Rosetta Stone, http://astron.berkeley.edu/~mwhite/rosetta/rosetta.html

6. P. Coles and F. Lucchin, Cosmology: The Origin and Evolution of Cosmic Structure, Wiley, New York, 1995.

7. Edward W. Kolb and Michael Turner, The Early Universe, Addison-Wesley, Reading, Massachusetts, 1990.

8. C. L. Bennett et al, First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results, available as astro-ph/0302207.

9. D. N. Spergel et al, First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters, available as astro-ph/0302209.

10. D. Pfenniger and D. Puy, Possible flakes of molecular hydrogen in the early Universe, available as astro-ph/0211393.

11. Andrzej Trautman, Pythagorean spinors and Penrose twistors, in The Geometric Universe: Science Geometry and the Work of Roger Penrose, eds. Huggett, Mason, Tod, Tsou and Woodhouse, Oxford U. Press, Oxford, 1998.

12. John Baez, OP¹ and Lorentzian geometry, http://math.ucr.edu/home/baez/Octonions/node11.html

week197

1. Workshop on categorification and higher-order geometry, http://www.math.ist.utl.pt/~rpicken/CHOG2003

2. Michael J. Hopkins, Topological modular forms, the Witten genus, and the theorem of the cube, in Proceedings of the International Congress of Mathematicians (Zurich, 1994), Birkhauser, Basel, 1995, pp. 554-565.

3. Stephan Stolz and Peter Teichner, What is an elliptic object? http://math.ucsd.edu/~teichner/Preprints/Oxford.pdf

4. Nils A. Baas, Bjorn Ian Dundas and John Rognes, Two-vector bundles and forms of elliptic cohomology, available as math.AT/0306027.

5. Nils A. Baas, Bjorn Ian Dundas and John Rognes, Two-vector bundles and forms of elliptic cohomology, available as math.AT/0306027.

6. Helena A. Verrill, Monstrous moonshine and mirror symmetry, http://hverrill.net/pages~helena/seminar/seminar1.html

7. Terry Gannon, Postcards from the edge, or Snapshots of the theory of generalised Moonshine, available as math.QA/0109067.

week198

1. David Corfield, Towards a Philosophy of Real Mathematics, Cambridge U. Press, Cambridge, 2003. More information and part of the book's introduction available at http://users.ox.ac.uk/~sfop0076/Towards.htm

2. John C. Baez, J. Daniel Christensen and Greg Egan, Asymptotics of 10j symbols, Class. Quant. Grav. 19 (2002) 6489-6513. Also available as gr-qc/0208010.

3. John W. Barrett and Christopher M. Steele, Asymptotics of relativistic spin networks, Class. Quant. Grav. 20 (2003) 1341-1362. Also available as gr-qc/0209023.

4. Laurent Freidel and David Louapre, Asymptotics of 6j and 10j symbols, Class. Quant. Grav. 20 (2003) 1267-1294. Also available as hep-th/0209134.

5. Robert Coquereaux, On the finite dimensional quantum group H = M₃ + M_2|1(Lambda²)₀, available as hep-th/9610114 and at http://www.cpt.univ-mrs.fr/~coque/articles_html/SU2qba/SU2qba.html

week190

1. J.-B. Bost and Alain Connes, "Hecke Algebras, Type III factors and phase transitions with spontaneous symmetry breaking in number theory", Selecta Math. (New Series), 1 (1995) 411-457.

2. Bernard L. Julia, Statistical theory of numbers, in Number Theory and Physics, eds. J. M. Luck, P. Moussa, and M. Waldschmidt, Springer Proceedings in Physics, Vol. 47, Springer-Verlag, Berlin, 1990, pp. 276-293. Summarized by Matthew Watkins in http://www.maths.ex.ac.uk/~mwatkins/zeta/Julia.htm

3. Matthew Watkins, http://www.maths.ex.ac.uk/~mwatkins/

4. Marcus du Sautoy, The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, HarperCollins, 2003.

5. Karl Sabbagh, The Riemann Hypothesis: the Greatest Unsolved Problem in Mathematics, Farrar Strauss & Giroux, 2003.

6. John Derbyshire, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem Mathematics, Joseph Henry Press, 2003.

7. Jeffrey Stopple, A Primer of Analytic Number Theory: from Pythagoras to Riemann, Cambridge U. Press, Cambridge, 2003.

8. Barry Cipra, A prime case of chaos, in What's Happening in the Mathematical Sciences, vol. 4, American Mathematical Society. Also available at http://www.maths.ex.ac.uk/~mwatkins/zeta/cipra.htm

9. Donald Spector, Supersymmetry and the Moebius inversion function, Communications in Mathematical Physics 127 (1990) 239-252.

10. Jonathan Rosenberg, K-theory and geometric topology, available at http://www.math.umd.edu/users/jmr/geomtop.pdf

11. C. Balteanu, Z. Fiedorowicz, R. Schwaenzl, and R. Vogt, Iterated monoidal categories, available at math.AT/9808082.

12. M. J. Shai Haran, The Mysteries of the Real Prime, Oxford U. Press, Oxford, 2001.

week200

1. John Baez, Higher-Dimensional Algebra, http://math.ucr.edu/home/baez/hda.html

2. Ramifications of Category Theory, http://ramcat.scform.unifi.it/

3. F. William Lawvere and Steve Schanuel, Conceptual Mathematics: A First Introduction to Categories, Cambridge U. Press, Cambridge, 1997.

4. F. William Lawvere and Robert Rosebrugh, Sets for Mathematics, Cambridge U. Press, Cambridge, 2002.

5. F. W. Lawvere, Functorial semantics of algebraic theories, Dissertation, Columbia University, 1963.

6. F. William Lawvere, Functorial semantics of algebraic theories, Proceedings, National Academy of Sciences, U.S.A. 50 (1963), 869-872.

7. Roy L. Crole, Categories for Types, Cambridge U. Press, Cambridge, 1993.

8. Michael Barr and Charles Wells, Toposes, Triples and Theories. Springer-Verlag, New York, 1983. Available for free electronically at http://www.cwru.edu/artsci/math/wells/pub/ttt.html

9. Maria Cristina Pedicchio, Algebraic Theories, in Textos de Matematica: School on Category Theory and Applications, Coimbra, July 13-17, 1999, pp. 101-159.

10. F. William Lawvere, Elementary theory of the category of sets, Proceedings of the National Academy of Science 52 (1964), 1506-1511.

11. F. William Lawvere, Algebraic theories, algebraic categories, and algebraic functors, in Theory of Models, North-Holland, Amsterdam (1965), 413-418.

12. F. William Lawvere, Functorial semantics of elementary theories, Journal of Symbolic Logic, Abstract, 31 (1966), 294-295.

13. F. William Lawvere, The category of categories as a foundation for mathematics, in La Jolla Conference on Categorical Algebra, Springer, Berlin 1966, pp. 1-20.

14. F. William Lawvere, Some algebraic problems in the context of functorial semantics of algebraic theories, in Reports of the Midwest Category Seminar, eds. Jean Benabou et al, Springer Lecture Notes in Mathematics No. 61, Springer, Berlin 1968, pp. 41-61.

15. F. William Lawvere, Ordinal sums and equational doctrines, Springer Lecture Notes in Mathematics No. 80, Springer, Berlin, 1969, pp. 141-155.

16. F. William Lawvere, Categorical dynamics, in Proceedings of Aarhus May 1978 Open House on Topos Theoretic Methods in Geometry, Aarhus/Denmark (1979).

17. F. William Lawvere, Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body, Cahiers de Topologie et Geometrie Differentielle Categorique 21 (1980), 337-392.

18. Anders Kock, Synthetic Differential Geometry, Cambridge U. Press, Cambridge, 1981.

19. F. William Lawvere and S. Schanuel, editors, Categories in Continuum Physics, Springer Lecture Notes in Mathematics No. 1174, Springer, Berlin, 1986.

20. F. William Lawvere, Foundations and applications: axiomatization and education, Bulletin of Symbolic Logic 9 (2003), 213-224. Also available at http://www.math.ucla.edu/~asl/bsl/0902/0902-006.ps

21. Colin McLarty, Elementary Categories, Elementary Toposes, Clarendon Press, Oxford, 1995.

22. R. Blackwell, G. M. Kelly, and A. J. Power, Two-dimensional monad theory, Jour. Pure Appl. Algebra 59 (1989), 1-41.

23. Brian Day and Ross Street, Monoidal bicategories and Hopf algebroids, Adv. Math. 129 (1997) 99-157.

24. F. Marmolejo, Doctrines whose structure forms a fully faithful adjoint string, Theory and Applications of Categories 3 (1997), 23-44. Available at http://www.tac.mta.ca/tac/volumes/1997/n2/3-02abs.html

25. S. Lack, A coherent approach to pseudomonads, Adv. Math. 152 (2000), 179-202. Also available at http://www.maths.usyd.edu.au:8000/u/stevel/papers/psm.ps.gz

26. Peter Johnstone, Sketches of an Elephant: a Topos Theory Compendium, Oxford U. Press, Oxford. Volume 1, comprising Part A: Toposes as Categories, and Part B: 2-categorical Aspects of Topos Theory, 720 pages, 2002. Volume 2, comprising Part C: Toposes as Spaces, and Part D: Toposes as Theories, 880 pages, 2002.

week201

1. Ian Stewart, Galois Theory, 3rd edition, Chapman and Hall, New York, 2004.

2. H. P. F. Swinnerton-Dyer, A Brief Guide to Algebraic Number Theory, Cambridge U. Press, Cambridge 2001.

3. Juergen Neukirch, Algebraic Number Theory, trans. Norbert Schappacher, Springer, Berlin, 1986.

4. K. Iwasawa, On solvable extensions of algebraic number fields, Ann. Math. 58 (1953) 548-572.

5. Pierre Deligne, Le groupe fondamental de la droite projective moins trois points, in Galois Groups over Q, MSRI Publications 16 (1989), 79-313.

6. Leila Schneps, The Grothendieck-Teichmueller group: a survey, in The Grothendieck Theory of Dessins D'Enfants, London Math. Society Notes 200, Cambridge U. Press, Cambridge 1994, pp. 183-204.

7. Leila Schneps, The Grothendieck-Teichmuller group and fundamental groups of moduli spaces, MSRI lecture available at http://www.msri.org/publications/ln/msri/1999/vonneumann/schneps/1/

   Grothendieck-Teichmueller group and Hopf algebras, MSRI lecture available at http://www.msri.org/publications/ln/msri/1999/vonneumann/schneps/2/

8. Pierre Cartier, A mad day's work: from Grothendieck to Connes and Kontsevich - the evolution of concepts of space and symmetry, Bulletin of the AMS, 38 (2001), 389 - 408. Also available at http://www.ams.org/joursearch/index.html

9. Jack Morava, The motivic Thom isomorphism, talk at the Newton Institute, December 2002, also available at math.AT/0306151.

© 2003 John Baez
baez@math.removethis.ucr.andthis.edu

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