Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, May 13, 2021.

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Thursday, May 13, 2021

2:00 pm in Zoom,Thursday, May 13, 2021

#### Five vertex models in enumerative and algebra combinatorics: Rogers-Ramanujan identities and LLT polynomials

###### Sylvie Corteel   [email] (University of California, Berkeley)

Abstract: The 5 vertex model is a very classical model related to Schur polynomials, reverse plane partitions, tilings of the Aztec diamond and many more combinatorial objects. Thanks to the Yang Baxter equation, one can prove symmetry of polynomials, (dual) Cauchy identities, partition functions... After reviewing the classical theory, I will generalize this model to a model on the cylinder and a colored 5 vertex model. I will explain how the cylindric partitions are related to Rogers Ramanujan identities and how we can discover new $A_2$ identities thanks to this approach. (This is joint work with J. Dousse, A. Uncu and T. Welsh). Then I will explain how colored models give a vertex model for LLT polynomials (This is joint work with A. Gitlin, D. Keating and J. Meza). Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.