|Date: Monday, January 22, 2018
Location: 3866 East Hall (4:00 PM to 5:00 PM)
Title: Class groups of cluster algebras
Abstract: We outline some recent work in arXiv/1712.06512. The authors note that the multiplicative/factorization structure of a cluster algebra is key for the proof of the Laurent phenomenon theorem for cluster algebras, and said structure is frequently leveraged in applications to representation theory and hyperbolic geometry. The preprint shows, among other things, that any cluster algebra that is a Krull domain has a finitely generated free abelian divisor class group--the latter being an invariant that governs the factorization theory of the ring. This result, Theorem 3.4, is roughly the halfway mark of the paper. In Section 5 of the paper, they cover more incisive results in the acyclic case, though I'll likely opt not to touch on that since this is a 31-page paper, that could easily be divvied up into a series of student combo talks!
Speaker: Robert Walker
Institution: University of Michigan