May 13, 2021, 2-3 pm CT
Speaker: Sylvie Corteel (UC Berkeley)
Title: Five vertex models in enumerative and algebra combinatorics :
Rogers-Ramanujan identities and LLT polynomials
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).
April 15, 2021, 2-3 pm CT
March 9, 2021, 10-11 am CT
Speaker: Ben Green (Oxford University)
Title: Open problems in additive combinatorics
Abstract: There will be discussion on some open problems, the audience is encouraged to look some in advance.
February 18, 2021, 2-3 pm CT
Speaker: Hao Huang (Emory)
Title: Interlacing methods in extremal combinatorics
Abstract: Extremal Combinatorics studies how large or how small a collection of finite objects could be, if it must satisfy certain restrictions. In this talk, we will discuss how eigenvalue interlacing lead to various interesting results in Extremal Combinatorics, including the Erdos-Ko-Rado Theorem and its degree version, an isodiametric inequality for discrete cubes, and the resolution of a thirty-year-old open problem in Theoretical Computer Science, the Sensitivity Conjecture. A number of open problems will be discussed during this talk.
January 21, 2021, 3-4 pm CT
Speaker: Stephanie van Willigenburg (University of British Columbia)
Title: The e-positivity of chromatic symmetric functions
Abstract: The chromatic polynomial was generalized to the chromatic symmetric function by Stanley in his seminal 1995 paper. This function is currently experiencing a flourishing renaissance, in particular the study of the positivity of chromatic symmetric functions when expanded into the basis of elementary symmetric functions, that is, e-positivity.
In this talk we approach the question of e-positivity from various angles. Most pertinently we resolve the 1995 statement of Stanley that no known graph exists that is not contractible to the claw, and whose chromatic symmetric function is not e-positive.
This is joint work with Soojin Cho, Samantha Dahlberg, Angele Foley and Adrian She, and no prior knowledge is assumed.