Cohomological Hall algebras for quiver with potential

Donaldson-Thomas theory has been developed to study moduli spaces in a 3-Calabi-Yau setting strongly related to superstring theory. It does not only apply to geometry but also to topology and to representation theory. The latter case is well-understood, and we start off by giving the definition and the main properties of the Cohomological Hall algebra for representations of quivers with potential. In the second part we sketch applications involving intersection cohomology of moduli spaces, quantum groups and Kac-Moody algebras. This is a report of joint work with Ben Davison and Markus Reineke.Non UBCUnreviewedAuthor affiliation: University of SheffieldPostdoctora