Abstract: The Cox ring of an algebraic variety (satisfying some natural conditions) is a very rich invariant.  It was introduced by Cox in 1995 for the study of toric varieties, and then generalized to normal varieties by  Arzhantsev, Berchtold and Hausen.

Abstract : Hall algebras and related notions play a prominent role in the modern representation theory. In their present form, they first appeared in a series of papers by Ringel on quantum groups. After giving all the necessary definitions, I will explain the interplay