MS Seminar (Mathematics - String Theory)

Speaker: Milen Yakimov (Louisiana State University)
Title: Double Bruhat cells, clusters and maximal green sequences
Date: Wed, Jan 25, 2017, 15:30 - 17:00
Place: Seminar Room A
Abstract: Cluster Algebras and their quantum counterparts are used in various settings in representation theory, geometry and mathematical physics. Maximal green sequences of cluster mutations were introduced by Keller in relation to Donaldson-Thomas invariants and dilogarithm identities, and by physicists in the study of BPS spectra. In this talk we will describe solutions of two problems on the representation theoretic aspects of cluster algebras. The first one is the Berenstein-Zelevinsky conjecture on the existence of quantum cluster algebra structures on the quantized coordinate rings of the double Bruhat cells in all symmetrizable Kac-Moody groups. The second one is the problem about existence of maximal green sequences for all such cluster algebras. The first part is a joint work with Ken Goodearl (University of California, Santa Barbara).