Michael Gekhtman (University of Notre Dame)
mgekhtma@nd.edu
I will present a construction that ties together of several diverse notions including spaces of periodic difference operators, Poisson submanifolds of a Drinfeld double of GL(n) and subsets of Grassmannians stable under the action of powers of a cyclic shift. The theory of generalized cluster algebras serves as a unifying theme. Time permitting, I will discuss potential applications to representation theory of quantum affine algebras at roots of unity. Based on a joint work with M. Shapiro and A. Vainshtein and an ongoing project with C. Fraser and K. Trampel.