# Hypergeometric and q-hypergeometric solutions of quantum differential equations

Date: Thursday, May 17, 2018 13:00 - 15:00
Speaker: Alexander Varchenko (University of North Carolina at Chapel Hill | UNC)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Tamas Hausel

### Abstract:

I will discuss hypergeometric and q-hypergeometric solutions of the equivariant quantum differential equations and associated qKZ difference equations for the cotangent bundle $T^*F_\lambda$ of a partial flag variety. These two types of solutions manifest two types of Landau-Ginzburg mirror symmetry for the cotangent bundle. I will discuss a "gamma theorem", which says the leading term of the asymptotics of the q-hypergeometric solutions can be written in terms of the equivariant gamma class of $T^*F_\lambda$. That statement is analogous to the statement of the gamma conjecture for Fano varieties by Galkin, Golyshev, and Iritani.