**Proceedings of Symposia in Pure Mathematics**

Volume: 73;
2005;
418 pp;
Hardcover

MSC: Primary 81; 57; 18; 53; 55; 37; 17;

Print ISBN: 978-0-8218-3666-8

Product Code: PSPUM/73

List Price: $103.00

AMS Member Price: $82.40

MAA Member Price: $92.70

**Electronic ISBN: 978-0-8218-9379-1
Product Code: PSPUM/73.E**

List Price: $103.00

AMS Member Price: $82.40

MAA Member Price: $92.70

# Graphs and Patterns in Mathematics and Theoretical Physics

Share this page *Edited by *
*Mikhail Lyubich; Leon Takhtajan*

The Stony Brook Conference, "Graphs and Patterns in Mathematics and Theoretical
Physics", was dedicated to Dennis Sullivan in honor of his sixtieth
birthday. The event's scientific content, which was suggested by Sullivan, was
largely based on mini-courses and survey lectures. The main idea was to help
researchers and graduate students in mathematics and theoretical physics who
encounter graphs in their research to overcome conceptual barriers.

The collection begins with Sullivan's paper, "Sigma models and string
topology," which describes a background algebraic structure for the sigma model
based on algebraic topology and transversality. Other contributions to the
volume were organized into five sections: Feynman Diagrams, Algebraic
Structures, Manifolds: Invariants and Mirror Symmetry, Combinatorial Aspects of
Dynamics, and Physics. These sections, along with more research-oriented
articles, contain the following surveys: "Feynman diagrams for pedestrians and
mathematicians" by M. Polyak, "Notes on universal algebra" by A. Voronov,
"Unimodal maps and hierarchical models" by M. Yampolsky, and "Quantum geometry
in action: big bang and black holes" by A. Ashtekar.

This comprehensive volume is suitable for graduate students and research
mathematicians interested in graph theory and its applications in mathematics
and physics.

#### Readership

Graduate students and research mathematicians interested in graph theory and its applications in mathematics and physics.

# Table of Contents

## Graphs and Patterns in Mathematics and Theoretical Physics

- Contents vii8 free
- Preface ix12 free
- Dennis Sullivan–A short history xiii16 free
- Dennis Sullivan's List of publications xv18 free
- Sigma models and string topology 124 free
- Feynman diagrams 1336
- Algebraic structures 79102
- Manifolds: invariants and mirror symmetry 149172
- Combinatorial aspects of dynamics 279302
- Physics 359382