Speaker: Andrey Smirnov (The University of North Carolina at Chapel Hill)

Where: In-Person at MIT Room 2-135, and on

Zoom: https://mit.zoom.us/j/93574730255 

Title: Frobenius intertwiners for q-difference equations

Abstract: 

The quantum difference equations are K-theoretic analogs of Dubrovin connection in quantum cohomology.

In my talk I show that over $p$-adic fields the quantum difference equations of Nakajima quiver varieties are equipped with the Frobenius automorphism $z\to z^p$.

I show that the corresponding Frobenius intertwiner is a partition function of quasimaps with special boundary conditions. I describe an explicit formula for the degree zero term of the intertwiner and explain the connection with works of Dwork, Sperber and Kedlaya.