Speaker: Michael Gekhtman (University of Notre Dame, USA)
Date and time: 20 May, 18.00 (Moscow time)
Title: Poisson-Lie Groups and Cluster Structures
Abstract: Coexistence of diverse mathematical structures supported on the same variety often leads to deeper understanding of its features. If the manifold is a Lie group, endowing it with a Poisson structure that respects group multiplication (Poisson– Lie structure) is instrumental in a study of classical and quantum mechanical systems with symmetries.
On the other hand, the ring of regular functions on certain Poisson varieties can have a structure of a cluster algebra. I will discuss natural cluster structures in the rings of regular functions on simple complex Lie groups and their homogenous spaces and Poisson–Lie/Poisson-homogeneous structures compatible with these cluster structures. Much of this talk is based on an ongoing collaboration with M. Shapiro and A. Vainshtein.
To access the online seminar please contact Anna Tolbey firstname.lastname@example.org