Event time:
Wednesday, February 23, 2022 - 4:15pm
Speaker:
Thomas Lam
Speaker affiliation:
University of Michigan
Event description:
Abstract:
A classical result states that the Poincare polynomial of a
Grassmannian manifold is given by a Gaussian polynomial, the
q-analogue of the binomial coefficient. I will discuss joint work
with Pasha Galashin where we prove a variant of this relating the
topology of a positroid variety and (q,t)-Catalan numbers. Positroid
varieties are remarkable subvarieties of the Grassmannian that have
made appearances in total positivity, scattering amplitudes, and
Schubert calculus. Our work relies on a connection between the
geometry of these spaces and link homology groups of certain
“positroid links”.