Francesco Sala

Hall algebras play a prominent role in the interactions between algebraic geometry and representation theory. Recently, "refined" versions of them, called K-theoretic Hall algebras, were introduced by Schiffmann and Vasserot. They have notable connections with the geometric Langlands correspondence, the theory of quantum groups and gauge theories.

In the present talk, I will give an overview of the theory of Hall algebras. Then I will describe some (new) examples of K-theoretic Hall algebras. These algebras are related to some stacks of a certain kind of sheaves on noncompact surfaces.  (Work in progress with Olivier Schiffmann.)