Mathematics

The present talk is devoted to a gentle introduction to the theory of cohomological Hall algebras (COHAs), how they arose from the study of the topology of moduli spaces, such as Hilbert schemes of points on smooth complex surfaces, and how they are connected to the theory of quantum groups, notably Yangians, the elliptic Hall algebra, quantum loop algebras, etc. In the second part of the talk, I will address the problem of constructing new representations of COHAs by using torsion pairs.