Positroids, knots, and Catalan numbers

Seminar: 
Colloquium
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”.