Tomasz Przezdziecki, Thorsten Beckmann, Soumyadip Sahu

Tomasz Przezdziecki (MPIM): Quiver Schur algebras and cohomological Hall algebras

I will discuss the connection between two algebras which first appeared in mathematics in very different contexts and were introduced with very different motivations, namely: quiver Schur algebras and cohomological Hall algebras. The former are a generalization of Khovanov-Lauda-Rouquier algebras, which play a crucial role in the categorification of quantum groups and their canonical bases. The latter were invented by Kontsevich and Soibelman as a categorification of Donaldson-Thomas invariants and as a step towards a rigorous definition of the algebra of BPS states from string theory. I will explain how quiver Schur algebras can be realized as algebras of certain operators on the CoHA, and generalize this relationship to quiver Schur algebras associated to quivers with a contravariant involution. I will also remark on the connection between quiver Schur algebras and affine q-Schur algebras appearing in the representation theory of p-adic groups.

Thorsten Beckmann (MPIM): Hyperkähler geometry

Soumyadip Sahu (MPIM): Modularity lifting theorems