GRAPHS AND PATTERNS
in Mathematics and Theoretical Physics A conference to celebrate Dennis Sullivan's
60^{th} birthday |

Department of Mathematics and Institute for Mathematical Sciences

Stony Brook, New York

June 14-21, 2001

A. Ashtekar |
J. Baez |
A. de Carvalho |
R. Forman |

K. Fukaya |
J. Hubbard |
D. Kreimer |
C. McMullen |

Y. Minsky |
M. Polyak |
N. Reshetikhin |
D. Sullivan |

D. Thurston |
B. Tsygan |
P. van Nieuwenhuizen |
A. Voronov |

Graphs occur as organizing objects in several fields of mathematics and theoretical physics. Each field interprets them in its own language. As a consequence, parallel developments are often played out in isolation from each other. The object of the conference was to present and try to bring together some or all of the following topics:

- I- Universal Algebra
- graphs and formal algebraic quantization;
- trees and operads;
- graph homology.

- II- Discrete Riemannian Geometry and Gauge Theory
- evaluating labeled graphs (spin networks);
- evaluating 3 dimensional embedded graphs with quantum group labelings;
- canonical quantization of general relativity via spin networks;
- the discrete spectrum of area and volume operators in quantum Riemannian geometry;
- path-integral quantization of general relativity via spin foams.

- III- Bifurcation Patterns in Dynamical Systems
- return times, kneading and renormalization;
- Hubbard trees, Yoccoz puzzles and the Mandelbrot set;
- train tracks and surface transformations.

- IV- Quantum Field Theory and Topology
- Feynman diagrams associated to an action functional;
- Chern-Simons diagrams and Vassiliev chord diagrams;
- BRST differential and renormalization;
- the knot-theoretic topological quantization of the algebra of graphs on surfaces;
- the Hopf algebra of trees and renormalization;
- combinatorial description of the monodromy of a rational conformal field theory;
- graphs and string theory;
- graphs and symplectic theory.

- V- Supersymmetry, Supergravity, and Superspace

**Conference Proceedings:**

We plan to publish a volume with the Proceedings of this conference. If you would like to submit a contribution, please contact any of the organizers. All contributions will be subject to review.

This event was sponsored by the James H. Simons Math-Physics Endowment and the National Science Foundation. |

The State University of New York at Stony Brook is an affirmative action/equal employment opportunity educator and employer. |