Speaker
Alex Takeda, Uppsala University
Abstract
There is a functorial perspective on TQFTs known generally by the name of the ‘cobordism hypothesis’, which encodes the data of such a topological theory in terms of a functor out of a category of bordisms, or equivalently a certain type of object in the target category. I will explain some of this perspective, and then talk about a relaxation of this definition, where the resulting theory is only defined on a certain class of bordisms. I will explain one such example, partially defined oriented 2d TQFTs, and show how the resulting algebraic structure, which can be expressed in terms of properads, appears in settings such as symplectic and algebraic geometry and string topology. I will present some of those examples appearing in my recent work. This talk is about joint papers with Kontsevich and Vlassopoulos, together with more recent unfinished work.