A new proof of positivity of DT invariants of symmetric quivers

https://hu-berlin.zoom.us/j/61686623112 [3]

I shall talk about a new interpretation of refined Donaldson-Thomas invariants of symmetric quivers, in particular re-proving their positivity (conjectured by Kontsevich and Soibelman, and proved by Efimov). This interpretation has two key ingredients. The first is a certain Lie (super-)algebra, for which we have two interpretations, in the context of Koszul duality theory and in the context of vertex Lie algebras. The second is an action of the Weyl algebra of polynomial differential operators on that Lie algebra, for which the characters of components of the space of generators give precisely the refined DT invariants. This is a joint project with Evgeny Feigin and Markus Reineke, partially relying on my recent work with Sergey Mozgovoy.