Speaker: Vasya Krylov (Harvard)

Title: Hikita conjectures for quiver theories and related structures

Abstract: Higgs and Coulomb branches of quiver gauge theories form two rich families of Poisson varieties that are expected to be exchanged by 3D mirror symmetry.
The Hikita conjectures relate the algebra and geometry of these branches in a nontrivial way, allowing one to extract new structures on one side by studying its mirror.
In this talk I will attempt to give an overview of the current state of the Hikita conjecture, with an emphasis on its interplay with other important structures such as representations of loop groups, the geometric Satake equivalence, the Riemann–Roch isomorphism, and twisted traces (time permitting).
I will illustrate how the picture works in the ADE case (where a lot can be proved) and formulate conjectures that generalize these observations to arbitrary quivers. Time permitting, I will explain a construction that extends some results beyond ADE. Talk will be based on joint works with Dinkins, Dumanski, Karpov, Lance, and Perunov as well as the results of many great mathematicians working in this field.

Zoom: https://mit.zoom.us/j/93615455445. For the Passcode, please contact Pavel Etingof at etingof@math.mit.edu.