Tuesday Seminar on Topology

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Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2022/11/01

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Minkyu Kim (The Univesity of Tokyo)
An obstruction problem associated with finite path-integral (JAPANESE)
[ Abstract ]
Finite path-integral introduced by Dijkgraaf and Witten in 1990 is a mathematical methodology to construct an Atiyah-Segal type TQFT from finite gauge theory. In three dimensions, it is generalized to Hopf algebra gauge theory of Meusburger, and the corresponding TQFT is known as Turaev-Viro model. On the one hand, the bicommutative Hopf algebra gauge theory is covered by homological algebra. In this talk, we will explain an obstruction problem associated with a refined finite path-integral construction of TQFT's from homological algebra. This talk is based on our study of a folklore claim in condensed matter physics that gapped lattice quantum system, e.g. toric code, is approximated by topological field theories in low temperature.
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html