Mikhail M. Kapranov's Books

Higher Category Theory

Workshop on Higher Category Theory and Physics, March 28-30, 1997, Northwestern University, Evanston, IL

By: Ezra Getzler,Mikhail M. Kapranov

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Higher Category Theory

Workshop on Higher Category Theory and Physics, March 28-30, 1997, Northwestern University, Evanston, IL

By: Ezra Getzler,Mikhail M. Kapranov

Comprises six presentations on new developments in category theory from the March 1997 workshop. The topics are categorification, computads for finitary monads on globular sets, braided n- categories and a-structures, categories of vector bundles and Yang- Mills equations, the role of Michael Batanin's monoidal globular categories, and braided deformations of monoidal categories and Vassiliev invariants. No index. Annotation copyrighted by Book News, Inc., Portland, OR.

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146

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821810561

ISBN 13

9780821810569

Discriminants, Resultants, and Multidimensional Determinants

By: Israel M. Gelfand,Mikhail Kapranov,Andrei Zelevinsky

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Discriminants, Resultants, and Multidimensional Determinants

By: Israel M. Gelfand,Mikhail Kapranov,Andrei Zelevinsky

This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory."—Mathematical Reviews

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529

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817647716

ISBN 13

9780817647711

Higher Segal Spaces

By: Tobias Dyckerhoff,Mikhail Kapranov

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Higher Segal Spaces

By: Tobias Dyckerhoff,Mikhail Kapranov

This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a simplicial space satisfying locality conditions related to triangulations of d-dimensional cyclic polytopes. Focus here is on the 2-dimensional case. Many important constructions are shown to exhibit the 2-Segal property, including Waldhausen’s S-construction, Hecke-Waldhausen constructions, and configuration spaces of flags. The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed. Higher Segal Spaces marks the beginning of a program to systematically study d-Segal spaces in all dimensions d. The elementary formulation of 2-Segal spaces in the opening chapters is accessible to readers with a basic background in homotopy theory. A chapter on Bousfield localizations provides a transition to the general theory, formulated in terms of combinatorial model categories, that features in the main part of the book. Numerous examples throughout assist readers entering this exciting field to move toward active research; established researchers in the area will appreciate this work as a reference.

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Page Count

230

Publisher

Springer Nature

Published Date

ISBN 10

3030271242

ISBN 13

9783030271244

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

By: Mikhail Lyubich,Leon Armenovich Takhtadzhi︠a︡n

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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

By: Mikhail Lyubich,Leon Armenovich Takhtadzhi︠a︡n

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.

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443

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821836668

ISBN 13

9780821836668

Discriminants, Resultants, and Multidimensional Determinants

By: Israel M. Gelfand,Mikhail Kapranov,Andrei Zelevinsky

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Discriminants, Resultants, and Multidimensional Determinants

By: Israel M. Gelfand,Mikhail Kapranov,Andrei Zelevinsky

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Solve jigsaw puzzle

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Page Count

529

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817647716

ISBN 13

9780817647711

Book's by Mikhail M. Kapranov

Higher Category Theory

Higher Category Theory

Discriminants, Resultants, and Multidimensional Determinants

Discriminants, Resultants, and Multidimensional Determinants

Higher Segal Spaces

Higher Segal Spaces

Graphs and Patterns in Mathematics and Theoretical Physics

Graphs and Patterns in Mathematics and Theoretical Physics

Discriminants, Resultants, and Multidimensional Determinants

Discriminants, Resultants, and Multidimensional Determinants

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