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Book DetailsProceedings of Symposia in Pure MathematicsVolume: 73; 2005; 418 ppMSC: Primary 81; 57; 18; 53; 55; 37; 17
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.
ReadershipGraduate students and research mathematicians interested in graph theory and its applications in mathematics and physics.
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Table of Contents
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Articles
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Dennis Sullivan — Sigma models and string topology [ MR 2131009 ]
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Feynman diagrams
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Michael Polyak — Feynman diagrams for pedestrians and mathematicians [ MR 2131010 ]
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Dirk Kreimer — Structures in Feynman graphs: Hopf algebras and symmetries [ MR 2131011 ]
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Algebraic structures
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Alexander A. Voronov — Notes on universal algebra [ MR 2131012 ]
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Dmitri Tamarkin and Boris Tsygan — The ring of differential operators on forms in noncommutative calculus [ MR 2131013 ]
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Vassily Gorbounov, Fyodor Malikov and Vadim Schechtman — Twisted chiral de Rham algebras on $\mathbb {P}^1$ [ MR 2131014 ]
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Manifolds: Invariants and mirror symmetry
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R. Kashaev and N. Reshetikhin — Invariants of tangles with flat connections in their complements [ MR 2131015 ]
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Stavros Garoufalidis and Jerome Levine — Tree-level invariants of three-manifolds, Massey products and the Johnson homomorphism [ MR 2131016 ]
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Kenji Fukaya — Multivalued Morse theory, asymptotic analysis and mirror symmetry [ MR 2131017 ]
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Combinatorial aspects of dynamics
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Robin Forman — Some applications of combinatorial differential topology [ MR 2131018 ]
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André de Carvalho — Extensions, quotients and generalized pseudo-Anosov maps [ MR 2131019 ]
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Michael Yampolsky — Unimodal maps and hierarchical models [ MR 2131020 ]
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Physics
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Abhay Ashtekar — Quantum geometry in action: Big bang and black holes [ MR 2131021 ]
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Peter van Nieuwenhuizen — Supersymmetry, supergravity, superspace and BRST symmetry in a simple model [ MR 2131022 ]
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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.
Graduate students and research mathematicians interested in graph theory and its applications in mathematics and physics.
-
Articles
-
Dennis Sullivan — Sigma models and string topology [ MR 2131009 ]
-
Feynman diagrams
-
Michael Polyak — Feynman diagrams for pedestrians and mathematicians [ MR 2131010 ]
-
Dirk Kreimer — Structures in Feynman graphs: Hopf algebras and symmetries [ MR 2131011 ]
-
Algebraic structures
-
Alexander A. Voronov — Notes on universal algebra [ MR 2131012 ]
-
Dmitri Tamarkin and Boris Tsygan — The ring of differential operators on forms in noncommutative calculus [ MR 2131013 ]
-
Vassily Gorbounov, Fyodor Malikov and Vadim Schechtman — Twisted chiral de Rham algebras on $\mathbb {P}^1$ [ MR 2131014 ]
-
Manifolds: Invariants and mirror symmetry
-
R. Kashaev and N. Reshetikhin — Invariants of tangles with flat connections in their complements [ MR 2131015 ]
-
Stavros Garoufalidis and Jerome Levine — Tree-level invariants of three-manifolds, Massey products and the Johnson homomorphism [ MR 2131016 ]
-
Kenji Fukaya — Multivalued Morse theory, asymptotic analysis and mirror symmetry [ MR 2131017 ]
-
Combinatorial aspects of dynamics
-
Robin Forman — Some applications of combinatorial differential topology [ MR 2131018 ]
-
André de Carvalho — Extensions, quotients and generalized pseudo-Anosov maps [ MR 2131019 ]
-
Michael Yampolsky — Unimodal maps and hierarchical models [ MR 2131020 ]
-
Physics
-
Abhay Ashtekar — Quantum geometry in action: Big bang and black holes [ MR 2131021 ]
-
Peter van Nieuwenhuizen — Supersymmetry, supergravity, superspace and BRST symmetry in a simple model [ MR 2131022 ]
