Categorification in geometry, topology, and physics
 Responsibility
 Anna Beliakova, Aaron D. Lauda, editors.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2017]
 Physical description
 x, 267 pages : illustrations ; 26 cm.
 Series
 Contemporary mathematics (American Mathematical Society) ; v. 684.
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA169 .C3746 2017  Unknown 
More options
Description
Creators/Contributors
 Contributor
 Beliakova, Anna, 1968 editor.
 Lauda, Aaron, 1981 editor.
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Contents

 * B. Webster, Geometry and categorification* Y. Li, A geometric realization of modified quantum algebras* T. Lawson, R. Lipshitz, and S. Sarkar, The cube and the Burnside category* S. Chun, S. Gukov, and D. Roggenkamp, Junctions of surface operators and categorification of quantum groups* R. Rouquier, KhovanovRozansky homology and 2braid groups* I. Cherednik and I. Danilenko, DAHA approach to iterated torus links.
 (source: Nielsen Book Data)
 Summary

The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorification is a powerful tool for relating various branches of mathematics and exploiting the commonalities between fields. It provides a language emphasizing essential features and allowing precise relationships between vastly different fields. This volume focuses on the role categorification plays in geometry, topology, and physics. These articles illustrate many important trends for the field including geometric representation theory, homotopical methods in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology. The companion volume (Contemporary Mathematics, Volume 683) is devoted to categorification and higher representation theory.
(source: Nielsen Book Data)
Subjects
 Subject
 Categories (Mathematics)
 Mathematical analysis.
 Topology.
 Geometry.
 Physics.
 Categories (Mathematics)
 Geometry.
 Mathematical analysis.
 Physics.
 Topology.
 Quantum theory > Groups and algebras in quantum theory > Quantum groups and related algebraic methods.
 Manifolds and cell complexes > Lowdimensional topology > Knots and links in $S^3$.
 Algebraic geometry > (Colo.)homology theory > Sheaves, derived categories of sheaves and related constructions.
 Category theory; homological algebra > Categories with structure > Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories.
 Global analysis, analysis on manifolds > Partial differential equations on manifolds; differential operators > Etainvariants, ChernSimons invariants.
 Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Applications to physics.
 Group theory and generalizations > Representation theory of groups > Hecke algebras and their representations.
 Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Homological methods in Lie (super)algebras.
 Nonassociative rings and algebras > Lie algebras and Lie superalgebras > KacMoody (super)algebras; extended affine Lie algebras; toroidal Lie algebras.
Bibliographic information
 Publication date
 2017
 Title Variation
 Categorification
 Series
 Contemporary mathematics ; 684
 ISBN
 9781470428211 (alkaline paper)
 1470428210 (alkaline paper)