Automata and pseudocharacters from one-dimensional TQFTs with defects

主讲人 Speaker:Mikhail Khovanov (Columbia University & Johns Hopkins University)
时间 Time:Fri., 16:00-17:00, April 19, 2024
地点 Venue:Lecture Hall C548, Shuangqing Complex Building A(清华大学双清综合楼A座C548报告厅); Zoom Meeting ID: 271 534 5558 Passcode: YMSC


TQFTs in dimensions two, three, and four have been at the forefront of developments in mathematics in the past three decades. In this light talk we will point out that even in dimension one TQFTs are interesting if one introduces defects. We will tell two stories:

I. Changing constants from a ground field to the Boolean semiring allows to interpret finite state automata as 1D TQFTs with defects with the free Boolean semimodule spanned by the states of an automaton as the value of the TQFT on a boundary point (joint work with P.Gustafson, M.S.Im, R.Kaldawy, and Z.Lihn).

II. Pseudocharacters and pseudorepresentations are an essential tool in modern number theory, discovered by A.Wiles and R.Taylor thirty years ago. We will explain that the pseudocharacter condition can be interpreted as lifting a 1D topological theory (a lax TQFT) to a TQFT and discuss an extension of that condition to higher dimensions (joint work with M.S.Im and V.Ostrik).

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