Roughly, a topological quantum field theory is a functor from a cobordism category to the category of vector spaces. The classical analogue should take values in symplectic manifolds instead of vector spaces. In this talk, Rajan Mehta will describe some ongoing work aimed at trying to characterize such functors in terms of algebraic and geometric data, including what is meant by 'symplectic category,' how the categories of spans and relations provide simple models for it, and how Frobenius objects in the categories of spans and relations correspond to simplicial sets satisfying certain conditions. This is based on various joint works with Ivan Contreras, Molly Keller, Adele Long, Sophia Marx, Walker Stern, and Ruoqi Zhang.
