#### Chandrasekhar Hall

#### Schubert calculus and Gelfand-Zetlin polytopes

#### Evgeny Smirnov

##### Higher School of Economics & Independent University of Moscow, Moscow, Russia

*We describe an approach to the Schubert calculus on full flag varieties*

using the volume polynomial associated with Gelfand-Zetlin polytopes. This

approach allows us to compute the intersection products of Schubert cycles

by intersecting faces of a polytope. We also prove a formula for the

Demazure characters of a given representation of GL(n) via exponential sums

over integral points in faces of the Gelfand-Zetlin polytope associated

with the representation. Time permitting, I will also discuss a (mostly

conjectural) generalization of our approach that would allow to describe

the K-theory of a full flag variety.

I am planning to introduce (or recall) all the definitions on flag

varieties during the talk, no prerequisites are necessary.

The talk is based on a joint work with V.Kiritchenko and V.Timorin.

Done