Quantum cohomology and mirror symmetry of flag varieties

Abstract: The quantum cohomology ring is a deformation of the ordinary cohomology ring that encodes enumerative geometry of curves. I will describe a natural map from a symmetric polynomial ring, which has a basis of Schur polynomials indexed by partitions, to the quantum cohomology ring of the partial flag variety, which has a basis of Schubert classes indexed by permutations or tuples of permutations. We will discuss surprising properties of this map and how this proves a mirror theorem for type A flag varieties. This is joint work with Elana Kalashnikov.

algebraic geometrycombinatorics

Audience: researchers in the discipline

MAAGC 2023

Series comments: The eighth annual Mid-Atlantic Algebra, Geometry, and Combinatorics (MAAGC) Workshop will take place Friday and Saturday, December 1-2, 2023 at Virginia Commonwealth University in Richmond, Virginia.

The MAAGC Workshop aims to bring together senior researchers and junior mathematicians from the region to exchange ideas and forge collaborations in algebra, geometry, and combinatorics. The conference is funded by National Science Foundation grant DMS-1728937.