Functional Analysis, Mathematical Physics, and Dynamical Systems

Generalized cluster structures and periodic difference operators

by Michael Gekhtman (Department of Mathematics, University of Notre Dame, USA)


I will present a construction that ties together of several diverse notions including spaces of periodic difference operators, Poisson sub manifolds 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.

Zoom link for lecture.

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