Graphs and Patterns in Mathematics and Theoretical Physics
Graphs and Patterns in Mathematics and Theoretical Physics

Author: Mikhail Lyubich

Publisher: American Mathematical Soc.

Published: 2005

Total Pages: 443

ISBN-13: 0821836668

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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.

Collected Papers of K.T. Chen
Collected Papers of K.T. Chen

Author: Kuo-Tsai Chen

Publisher: Springer Science & Business Media

Published: 2001-06-21

Total Pages: 776

ISBN-13: 9780817640057

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Kuo-Tsai Chen (1923-1987) is best known to the mathematics community for his work on iterated integrals and power series connections in conjunction with his research on the cohomology of loop spaces. His work is intimately related to the theory of minimal models as developed by Dennis Sullivan, whose own work was in part inspired by the research of Chen. An outstanding and original mathematician, Chen's work falls naturally into three periods: his early work on group theory and links in the three sphere; his subsequent work on formal differential equations, which gradually developed into his most powerful and important work; and his work on iterated integrals and homotopy theory, which occupied him for the last twenty years of his life. The goal of Chen's iterated integrals program, which is a de Rham theory for path spaces, was to study the interaction of topology and analysis through path integration. The present volume is a comprehensive collection of Chen's mathematical publications preceded by an article, "The Life and Work of Kuo-Tsai Chen," placing his work and research interests into their proper context and demonstrating the power and scope of his influence.