Title: Hall Algebras and Quantum Groups
Program: Integrability in Modern Theoretical and Mathematical Physics
Speaker: Mike Gorsky, Jussieu Paris
Date: Wednesday, December 12, 2012
Time: 4:00pm – 5:00pm
Place: Seminar Room 313, Simons Center
Abstract: We will discuss how the concept of Hall algebras of abelian and exact categories is related to the theory of quantum groups. The theorems of Ringel and M. Greene recover the nilpotent part of the quantum group from the Hall algebra of the category of representations of the corresponding quiver. These results motivated work of G. Lusztig on canonical bases. Recently Bridgeland constructed the whole quantum group via categories of Z_2-graded complexes. If time permits, I will say a few words on the generalization of his construction.