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Topological Field Theory, Higher Categories, and Their Applications

Kapustin, Anton (2010) Topological Field Theory, Higher Categories, and Their Applications. In: ICM Proceedings. No.3. Hindustan Book Agency , New Delhi, pp. 2021-2043. ISBN 9789814324335. https://resolver.caltech.edu/CaltechAUTHORS:20160503-151154407

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Abstract

It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n > 1. Recently the physical meaning of these higher categorical structures has been recognized and concrete examples of Extended TFTs have been constructed. Some of these examples, like the Rozansky-Witten model, are of geometric nature, while others are related to representation theory. I outline two application of higher-dimensional TFTs. One is related to the problem of classifying monoidal deformations of the derived category of coherent sheaves, and the other one is geometric Langlands duality.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1004.2307arXivDiscussion Paper
http://www.mathunion.org/ICM/ICM2010.3/PublisherArticle
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2010 Hindustan Book Agency. Submitted on 14 Apr 2010 (v1), last revised 22 Apr 2010 this version, (v2). I would like to thank David Ben-Zvi, Dmitri Orlov, and Lev Rozansky for comments on the draft of the talk.
Subject Keywords:Topological field theory, 2-categories, monoidal categories, derived category of coherent sheaves, geometric Langlands duality
Issue or Number:3
Classification Code:Mathematics Subject Classification (2000). Primary 81T45; Secondary 18D05.
Record Number:CaltechAUTHORS:20160503-151154407
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160503-151154407
Official Citation:Anton Kapustin Topological Field Theory, Higher Categories, and Their Applications 2021-2043
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66625
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:04 May 2016 21:05
Last Modified:03 Oct 2019 09:58

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