Hidden algebraic structures in geometry from quantum field theory

Speaker

Du Pei is currently an associate professor of quantum mathematics at the University of Southern Denmark. He obtained his Ph.D. in theoretical physics in 2016 from Caltech. His main research interests concern the geometric, algebraic and categorical properties of quantum field theory.

Abstract

The existence of quantum field theories in higher dimensions predicts many hidden algebraic structures in geometry and topology. In this talk, I will survey some recent developments where such algebraic structures lead to new insights into 1) the quantization of moduli spaces of Higgs bundles, 2) the categorification of quantum invariants of 3-manifolds, and 3) novel types of TQFTs in four dimensions.