Lorenzo Riva: Topological field theories in algebraic topology and mathematical physics

Lorenzo Riva (Notre Dame)

Title: Topological field theories in algebraic topology and mathematical physics

Abstract: We learned a long time ago, for example from Thom's work, that there is a connection between bordism theory and homotopy theory that allows us to better understand smooth manifolds. One natural extension of the work of Thom is obtained by studying a higher category of bordisms and its associated representations, which for historical reasons are called (functorial) topological field theories (TFTs). This historical connection to mathematical physics has not ceased to be relevant: there are many classical and quantum field theories of mathematical interest which are conjectured to yield functorial TFTs that yield computable(ish) invariants of manifolds. In this talk we will explore one such example, given by the Rozansky-Witten models [Witten 1997] as categorified in [Kapustin, Rozansky, Saulina], and see how it works out in a fully coherent (i.e. infinity-categorical) setting.