Quadratic algebras and DT invariants of symmetric quivers

For each symmetric quiver, Kontsevich and Soibelman defined a collection of rational numbers, the "refined Donaldson-Thomas invariants". They conjectured that those numbers are in fact non-negative integers, which was first proved by Efimov. In this talk, I shall explain a new approach to studying these numbers, inspired by various aspects of the Koszul duality theory for associative algebras. In particular, this approach leads to a new family of quadratic algebras which are conjectured to be Koszul and are proved to satisfy the "numerical Koszulness" criterion. Time permitting, I shall discuss various particular cases in which the conjecture is proved, and some interesting combinatorics related to those cases. This talk is based on joint work with Evgeny Feigin and Markus Reineke.