Abstract: 

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).

Speaker's website: http://math.columbia.edu/~khovanov/ 

Video： http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Automata_and_pseudocharacters_from_one_dimensional_TQFTs_with_defects.html