Department of

# Mathematics

Seminar Calendar
for Combinatorics Colloquium events the year of Sunday, April 11, 2021.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      March 2021             April 2021              May 2021
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6                1  2  3                      1
7  8  9 10 11 12 13    4  5  6  7  8  9 10    2  3  4  5  6  7  8
14 15 16 17 18 19 20   11 12 13 14 15 16 17    9 10 11 12 13 14 15
21 22 23 24 25 26 27   18 19 20 21 22 23 24   16 17 18 19 20 21 22
28 29 30 31            25 26 27 28 29 30      23 24 25 26 27 28 29
30 31


Thursday, January 21, 2021

3:00 pm in Zoom,Thursday, January 21, 2021

#### The e-positivity of chromatic symmetric functions

###### Stephanie van Willigenburg   [email] (University of British Columbia)

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. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Thursday, February 18, 2021

2:00 pm in Zoom,Thursday, February 18, 2021

#### Interlacing methods in extremal combinatorics

###### Hao Huang (Emory University)

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.

Tuesday, March 9, 2021

10:00 am in Zoom,Tuesday, March 9, 2021

#### Open problems in additive combinatorics

###### Ben Green (Oxford University)

Abstract: There will be discussion on some open problems, the audience is encouraged to look some in advance.

Thursday, April 15, 2021

2:00 pm in Zoom,Thursday, April 15, 2021

#### Flat Littlewood polynomials exist

###### Robert Morris (IMPA, Brazil)

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.