%0 Generic %1 Kapustin2010 %A Kapustin, Anton %D 2010 %K categories field theory topological %T Topological Field Theory, Higher Categories, and Their Applications %U http://arxiv.org/abs/1004.2307 %X 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.

@misc{Kapustin2010, 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. }, added-at = {2010-04-28T20:23:36.000+0200}, author = {Kapustin, Anton}, biburl = {https://www.bibsonomy.org/bibtex/27a404a6c82a4fcb3b1fddae1fd2b20e5/uludag}, description = {Topological Field Theory, Higher Categories, and Their Applications}, interhash = {b3cd1c4dd9ede347c08061f476814969}, intrahash = {7a404a6c82a4fcb3b1fddae1fd2b20e5}, keywords = {categories field theory topological}, note = {cite arxiv:1004.2307 Comment: 22 pages, latex, 9 pdf figures. To appear in the Proceedings of ICM 2010.}, timestamp = {2010-04-28T20:23:36.000+0200}, title = {Topological Field Theory, Higher Categories, and Their Applications}, url = {http://arxiv.org/abs/1004.2307}, year = 2010 }