Proceedings of Symposia in Pure Mathematics 2005; 418 pp; hardcover Volume: 73 ISBN10: 0821836668 ISBN13: 9780821836668 List Price: US$103 Member Price: US$82.40 Order Code: PSPUM/73
 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 minicourses 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 researchoriented 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  D. Sullivan  Sigma models and string topology
Feynman diagrams  M. Polyak  Feynman diagrams for pedestrians and mathematicians
 D. Kreimer  Structures in Feynman graphs: Hopf algebras and symmetries
Algebraic structures  A. A. Voronov  Notes on universal algebra
 D. Tamarkin and B. Tsygan  The ring of differential operators on forms in noncommutative calculus
 V. Gorbounov, F. Malikov, and V. Schechtman  Twisted chiral de Rham algebras on \(\mathbb{P}^1\)
Manifolds: Invariants and mirror symmetry  R. Kashaev and N. Reshetikhin  Invariants of tangles with flat connections in their complements
 S. Garoufalidis and J. Levine  Treelevel invariants of threemanifolds, Massey products and the Johnson homomorphism
 K. Fukaya  Multivalued Morse theory, asymptotic analysis and mirror symmetry
Combinatorial aspects of dynamics  R. Forman  Some applications of combinatorial differential topology
 A. de Carvalho  Extensions, quotients and generalized pseudoAnosov maps
 M. Yampolsky  Unimodal maps and hierarchical models
Physics  A. Ashtekar  Quantum geometry in action: big bang and black holes
 P. van Nieuwenhuizen  Supersymmetry, supergravity, superspace and BRST symmetry in a simple model
