Abstract:

In this talk, I would like you to meet Hall-Littlewood-Schubert series, a new class of multivariate generating functions. Their definition features semistandard Young tableaux and polynomials resembling the classical Hall-Littlewood polynomials. Their intrinsic beauty notwithstanding, Hall-Littlewood-Schubert series have many applications to counting problems in algebra, geometry, and number theory. In my talk the spotlight will be on applications to affine Schubert series. These may be seen as an integral analogue of the Poincare polynomials enumerating the rational points over finite fields of classical Schubert varieties. The latter parametrize subspaces of a given vector space by the intersection dimensions with a fixed flag of reference. This work is joint with Joshua Maglione. I will explain things from scratch, assuming no familiarity with the advanced technical vocabulary used in this abstract.