Pacific Institute for the Mathematical Sciences - PIMS

From hopping particles to Macdonald and Schubert polynomials [Video]

The asymmetric exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice. While it was initially introduced by Macdonald-Gibbs-Pipkin to provide a model for translation in protein synthesis, the stationary distribution of the ASEP and its variants has surprising connections to combinatorics. I will explain how the study of the ASEP on a ring leads to new formulas for Macdonald polynomials, a remarkable family of multivariate polynomials which generalize Schur polynomials. In a different direction, the inhomogeneous ASEP on a ring is closely connected to Schubert polynomials, which represent classes of Schubert varieties in the flag variety. This talk is based on joint work with Corteel-Mandelshtam, and joint work with Donghyun Kim.

Speaker Biography: Lauren Williams is the Dwight Parker Robinson Professor of Mathematics at Harvard University and the Sally Starling Seaver Professor at the Radcliffe Institute. She is a leader in the field of algebraic combinatorics, with research programs on the positive Grassmannian, and combinatorial models in statistical mechanics. Before moving to Harvard, she was a professor at Berkeley, where she held numerous prestigious prizes and grants including a Sloan fellowship and an NSF Career grant. In a recent Quanta article on her work, she was described as fearless, for her willingness to take mathematical leaps.

About the series:    

Starting in 2021, PIMS has inaugurated a high-level network-wide colloquium series. Distinguished speakers will give talks across the full PIMS network with one talk per month during the academic term. The 2021 speaker series is part of the PIMS 25th Anniversary showcase.

Time:

All network wide colloquia take place at 1:30pm Pacific Time 

Registration: 

To attend this event please register here. Kindly note that this talk will be recorded.