UBC

Tue 19 Nov 2019, 4:00pm
Discrete Math Seminar
ESB 4127

The epositivity of chromatic symmetric functions

ESB 4127
Tue 19 Nov 2019, 4:00pm5:00pm
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, epositivity.
In this talk we approach the question of epositivity 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 epositive.
This is joint work with Soojin Cho, Samantha Dahlberg, Angele Foley and Adrian She, and no prior knowledge is assumed.
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University of Queensland

Tue 14 Jan 2020, 4:00pm
Discrete Math Seminar
ESB 4127

Lascoux polynomials and colored vertex models

ESB 4127
Tue 14 Jan 2020, 4:00pm5:00pm
Abstract
The cohomology ring of the Grassmannian, the set of kdimensional subspaces in ndimensional space, can be described by Schur functions, a symmetric function that are characters of the special linear Lie group. To study the Ktheory ring, the corresponding objects we use are (symmetric) Grothendieck polynomials. Demazure characters can be considered as partial Schur functions and are characters of representations of the subgroup of upper triangular matrices. The Ktheoretic analog of Demazure characters are known as Lascoux polynomials, but they currently have no representation theoretic or geometric interpretation. In joint work with Valentin Buciumas and Katherine Weber, we give the first known combinatorial interpretation for Lascoux polynomials by describing a colored version of the 5vertex model of Motegi and Sakai. In this talk, we will discuss Lascoux polynomials, the colored 5vertex model, and the corresponding combinatorial interpretation from our result. No knowledge of the material will be assumed.
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