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Graphs and patterns in mathematics and theoretical physics : proceedings of the Conference on Graphs and Patterns in Mathematics and Theoretical Physics, dedicated to Dennis Sullivan's 60th birthday, June 14-21, 2001, Stony Brook University, Stony Brook, NY / Mikhail Lyubich, Leon Takhtajan, editors.
- Format:
- Book
- Conference/Event
- Conference Name:
- Conference on Graphs and Patterns in Mathematics and Theoretical Physics (2001 : Stony Brook University), issuing body.
- Series:
- Proceedings of symposia in pure mathematics ; volume 73.
- Proceedings of symposia in pure mathematics ; volume 73
- Language:
- English
- Subjects (All):
- Graph theory--Congresses.
- Graph theory.
- Mathematics--Graphic methods--Congresses.
- Mathematics.
- Physics--Graphic methods--Congresses.
- Physics.
- Manifolds (Mathematics)--Congresses.
- Manifolds (Mathematics).
- Physical Description:
- 1 online resource (443 p.)
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2005]
- Language Note:
- English
- Summary:
- 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.
- Contents:
- ""Contents""; ""Preface""; ""Dennis Sullivan�A short history""; ""Dennis Sullivan's List of publications""; ""Sigma models and string topology""; ""Feynman diagrams""; ""Feynman diagrams for pedestrians and mathematicians""; ""Structures in Feynman graphs: Hopf algebras and symmetries""; ""Algebraic structures""; ""Notes on universal algebra""; ""The ring of differential operators on forms in noncommutative calculus""; ""Twisted chiral de Rham algebras on P1""; ""Manifolds: invariants and mirror symmetry""; ""Invariants of tangles with flat connections in their complements""
- ""Tree-level invariants of three-manifolds, Massey products and the Johnson homomorphism""""Multivalued Morse theory, asymptotic analysis and mirror symmetry""; ""Combinatorial aspects of dynamics""; ""Some applications of combinatorial differential topology""; ""Extensions, quotients and generalized pseudo-Anosov maps""; ""Unimodal maps and hierarchical models""; ""Physics""; ""Quantum geometry in action: big bang and black holes""; ""Supersymmetry, supergravity, superspace and BRST symmetry in a simple model""
- Notes:
- Description based upon print version of record.
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 0-8218-9379-3
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