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Generalized cluster structures and periodic difference operators
Algebraic Geometry and Number Theory| Speaker: | Michael Gekhtman, University of Notre Dame |
| Related Webpage: | https://math.nd.edu/people/faculty/michael-gekhtman/ |
| Location: | 2112 MSB |
| Start time: | Wed, Apr 13 2022, 11:00AM |
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.