Speaker: Dmytro Voloshyn
IBS Center for Geometry and Physics, Pohang
Will give a Algebraic Geometry and Commutative Algebra Seminar entitled:
Generalized cluster structures on the special linear group
Abstract: The Gekhtman-Shapiro-Vainshtein conjecture (the GSV conjecture) states that for any given simple complex algebraic group G and any Poisson bracket from the Belavin-Drinfeld class, there exists a compatible generalized cluster structure. In this talk, I will review the process of constructing compatible generalized cluster structures, as well as the current state-of-the-art on the GSV conjecture. After that, I will describe a construction of generalized cluster structures on SL(n) compatible with Poisson brackets induced from the Poisson dual of SL(n) endowed with the Poisson structure determined by a BD triple of type An-1. I will also describe the associated family of birational quasi-isomorphisms. The talk will be based on the preprint arXiv:2312.04859 (joint work with M. Gekhtman).
Date: 04-25-2024
Time: 3:30 pm
Location: 258 Hurley Bldg