# philadelphia-2016-abstracts

MAAGC 2016 ABSTRACTS

Anders Buch (Rutgers):

Title: Quantum K-theory of cominuscule flag varieties

Abstract: The (small) quantum K-theory ring of a flag variety X = G/P is a formal deformation of the ordinary K-theory ring that encodes the K-theoretic Gromov-Witten invariants of X (3 point, genus zero). These Gromov-Witten invariants are challenging to compute for general flag varieties, but for cominuscule flag varieties they are equal to triple intersections on related flag varieties by the `quantum equals classical' theorem. Cominuscule varieties have the additional advantage that their Schubert classes can be described with diagrams of boxes that generalize the Young diagrams known from the Schubert calculus of classical Grassmannians. I will speak about what we know about the quantum K-theory of cominuscule varieties, including a type-uniform Chevalley formula that uniquely determines the equivariant quantum K-theory ring. This talk is based on joint work with P.-E. Chaput, L. Mihalcea, and N. Perrin.

Rebecca Goldin (George Mason):

Title: Positivity in Schubert Calculus

Abstract: I will talk about positivity in Schubert calculus in equivariant cohomology and possibly K-theory, with a discussion of the underlying geometry.

Jim Haglund (Penn) / Adriano Garsia (UCSD):

Title: Some Outstanding open Problems for our new Problem Solvers

Abstract: The ecent solution of the Compositional Shuffle conjecture by Erik Carlsson and Anton Mellit, the solution of the sweep map conjectures by Nathan Wiliams and now the solution by Anton Mellit of the Rational Compositional Shuffle Conjecture may lead some of our less informed Algebraic Combinatorists to the conclusion that there is nothing left to do in our subject. Nothing could be further from the truth. This talk is only to give a glimpse of the fact that our panorama of open problems is actually exponentially increasing.

Thomas Lam (Michigan):

Title: Dimers and Canonical Bases

Abstract: I will talk about algebraic aspects of perfect matchings in planar graphs, or equivalently, the "dimer model". I will explain how canonical bases from representation theory can be applied to the study of dimers.