An introduction to the BPS cohomolgy of 2-Calabi—Yau categories

BPS cohomology is a cohomological invariant of sufficently geometric abelian categories of homological dimension 1,2, or 3 and has its origins in the enumerative geometry of Calabi—Yau threefolds. Nowadays there are many applications of BPS cohomology, especially to (geometric) representation theory.

The aim of the talk is to give an overview of my joint work with Ben Davison and Lucien Hennecart on the BPS cohomolgy of 2-Calabi—Yau categories and its applications. We will begin by counting vector spaces and hopefully end by talking about non-abelian Hodge theory for moduli stacks.