Exact structures and degeneration of Hall algebras

Hall algebras and various related structures play a prominent role in the modern representation theory. I will explain the interplay between different exact structures on an additive category and degenerations of the associated Hall algebras. For the categories of representations of Dynkin quivers, this recovers degenerations of the negative part of the corresponding quantum group. I will sketch the proofs of our results in the general case based on Auslander-Reiten theory. We will discuss further examples related to quantum doubles of quantum Borel subalgebras and, if time permits, certain generalizations involving extriangulated categories. (Based on joint work with Xin Fang.)