Positroids, knots, and Catalan numbers

Wed Feb 23, 2022 4:15 p.m.—5:15 p.m.
Exterior of Sheffield-Sterling-Strathcona Hall featuring a stone carving of Yale's coat of arms and motto

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Seminar: 
Colloquium

Event time: 
Wednesday, February 23, 2022 - 4:15pm

Speaker: 
Thomas Lam

Speaker affiliation: 
University of Michigan 

Event description: 
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”.