On the Hall algebra constructionMPIM

by Jonte Gödicke (MPIM)

Thursday Mar 26, 2026, 3:00 PM → 4:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

MPI-Oberseminar

Hall algebras, appearing in different incarnations, play an important role in classical representation theory, as they describe interesting algebras, like the algebra of symmetric functions and quantum groups. Broadly speaking, the Hall algebra construction associates to an abelian category A an algebra of functions on the moduli of objects M(A) of A. This forms an instance of a more general construction that turns categorical into algebraic data using geometry.

The goal of this talk is to describe this construction and its categorification in detail and to explain why such a categorified Hall algebra construction is desirable from the perspective of categorified representation theory.