September 12, Wednesday, 15:30, room 306

Evgeny Smirnov

Schubert varieties and Schubert polynomials

I am going to speak about Schubert varieties on a full flag variety. These varieties play an important role in enumerative geometry. The geometric problem of intersecting Schubert varieties (in general position) has its algebraic counterpart, dealing with Schubert polynomials. So a geometric question can be reduced to a purely algebraic/combinatorial one. I am planning to define Schubert polynomials combinatorially (in two different ways). Time permitting, I will speak about the results of Knutson and Miller (2005) who showed how Schubert polynomials appear in the context of Gröbner degeneration of Schubert varieties.

No preliminary knowledge of Schubert calculus is required, all necessary definitions will be given during the talk.