Mikhail Kapranov's Books

Higher Segal Spaces

By: Tobias Dyckerhoff,Mikhail Kapranov

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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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230

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Springer Nature

Published Date

ISBN 10

3030271242

ISBN 13

9783030271244

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

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Springer Science & Business Media

Published Date

ISBN 10

0817647716

ISBN 13

9780817647711

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

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

Laminations and Foliations in Dynamics, Geometry and Topology

Proceedings of the Conference on Laminations and Foliations in Dynamics, Geometry and Topology, May 18-24, 1998, SUNY at Stony Brook

By: Mikhail Lyubich,John Willard Milnor,Yair Nathan Minsky

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Laminations and Foliations in Dynamics, Geometry and Topology

Proceedings of the Conference on Laminations and Foliations in Dynamics, Geometry and Topology, May 18-24, 1998, SUNY at Stony Brook

By: Mikhail Lyubich,John Willard Milnor,Yair Nathan Minsky

This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research fields with little interaction among practitioners. The conference brought together the diverse points of view of researchers from different areas. This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event. Of particular interest are the articles by F. Bonahon, "Geodesic Laminations on Surfaces", and D. Gabai, "Three Lectures on Foliations and Laminations on 3-manifolds", which are based on minicourses that took place during the conference.

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Page Count

250

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821819852

ISBN 13

9780821819852

Abelian Galois Cohomology of Reductive Groups

By: Mikhail Borovoi

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Abelian Galois Cohomology of Reductive Groups

By: Mikhail Borovoi

In this volume, a new function H 2/ab (K, G) of abelian Galois cohomology is introduced from the category of connected reductive groups G over a field K of characteristic 0 to the category of abelian groups. The abelian Galois cohomology and the abelianization map ab1: H1 (K, G) -- H 2/ab (K, G) are used to give a functorial, almost explicit description of the usual Galois cohomology set H1 (K, G) when K is a number field

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American Mathematical Soc.

Published Date

ISBN 10

0821806505

ISBN 13

9780821806500

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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529

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Springer Science & Business Media

Published Date

ISBN 10

0817647716

ISBN 13

9780817647711

Topology and K-Theory

Lectures by Daniel Quillen

By: Robert Penner

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Topology and K-Theory

Lectures by Daniel Quillen

By: Robert Penner

These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980. He had just received the Fields Medal for his work on these topics among others and was funny and playful with a confident humility from the start. These are not meant to be polished lecture notes, rather, things are presented as did Quillen reflected in the hand-written notes, resisting any temptation to change or add notation, details or elaborations. Indeed, the text is faithful to Quillen's own exposition, even respecting the {\sl board-like presentation} of formulae, diagrams and proofs, omitting numbering theorems in favor of names and so on. This is meant to be Quillen on Quillen as it happened forty years ago, an informal text for a second-semester graduate student on topology, category theory and K-theory, a potential preface to studying Quillen's own landmark papers and an informal glimpse of his great mind. The intellectual pace of the lectures, namely fast and lively, is Quillen himself, and part of the point here is to capture some of this intimacy. To be sure, much has happened since then from this categorical perspective started by Grothendieck, and Misha Kapranov has contributed an Afterword in order to make it more useful to current students.

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201

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Springer Nature

Published Date

ISBN 10

3030439968

ISBN 13

9783030439965

Higher Segal Spaces

By: Tobias Dyckerhoff,Mikhail Kapranov

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Higher Segal Spaces

By: Tobias Dyckerhoff,Mikhail Kapranov

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230

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Springer Nature

Published Date

ISBN 10

3030271242

ISBN 13

9783030271244

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

Average ratings

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Write a review

Solve jigsaw puzzle

Age

Page Count

146

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821810561

ISBN 13

9780821810569

Book's by Mikhail Kapranov

Higher Segal Spaces

Higher Segal Spaces

Discriminants, Resultants, and Multidimensional Determinants

Discriminants, Resultants, and Multidimensional Determinants

Higher Category Theory

Higher Category Theory

Graphs and Patterns in Mathematics and Theoretical Physics

Graphs and Patterns in Mathematics and Theoretical Physics

Laminations and Foliations in Dynamics, Geometry and Topology

Laminations and Foliations in Dynamics, Geometry and Topology

Abelian Galois Cohomology of Reductive Groups

Abelian Galois Cohomology of Reductive Groups

Discriminants, Resultants, and Multidimensional Determinants

Discriminants, Resultants, and Multidimensional Determinants

Topology and K-Theory

Topology and K-Theory

Higher Segal Spaces

Higher Segal Spaces

Higher Category Theory

Higher Category Theory

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