Speaker:
Valentina Kirichenko
Introductory talk at SMUGA, April 2th, 2014:
Title:
Divided difference operators, flags and pipe-dreams
Abstract:
Divided differences first emerged as discrete analogs of derivatives. In the 1970s, Demazure and Bernstein-I.Gelfand-S.Gelfand used divided difference operators on polynomials to obtain formulas for the Schubert cycles in the Borel presentation for the cohomology rings of varieties of complete flags. Since then divided difference operators played an important role in Schubert calculus, both in the geometric and combinatorial setting. I will talk about different aspects of divided difference operators including their geometric meaning in terms of push-pull operators and combinatorial interpretation in terms of mitosis on pipe-dreams.
Research talks at IMPANGA (2 talks), April 4th, 2014:
Title:
Demazure operators and Okounkov polytopes of Bott-Samelson resolutions
Abstract:
Demazure operators are representation-theoretic versions of divided difference operators. I will talk about a convex-geometric realization of Demazure operators that yields analogs of string polytopes (such as Gelfand-Zetlin polytopes). Conjecturally, these polytopes coincide with Okounkov polytopes of line bundles on complete flag varieties for a natural choice of geometric valuation. More generally, I will formulate a conjecture about Okounkov polytopes of Bott-Samelson resolutions of Schubert varieties.
