Department of

# Mathematics

Seminar Calendar
for Combinatorics Colloquium events the year of Friday, December 3, 2021.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
    November 2021          December 2021           January 2022
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1  2  3  4  5  6             1  2  3  4                      1
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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)

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.

Tuesday, September 7, 2021

11:00 am in 347 Altgeld Hall,Tuesday, September 7, 2021

#### Degenerate Turan problems for graphs

###### Tao Jiang   [email] (Miami University of Ohio)

Abstract: In Turan type extremal problems, we want to determine how dense a graph or hypergraph is without containing a particular subgraph or family of subgraphs. Such problems are central to extremal graph theory, because solving them requires one to thoroughly investigate the interaction of global graph parameters with local structures. Efforts in solving these problems have spurred the developments of some powerful tools in extremal graph theory, such as the regularity method, probabilistic and algebraic methods.

While Turan problems have satisfactory solutions for non-bipartite graphs, the problem is still generally wide-open for bipartite graphs with many intriguing conjectures and results. In this talk, we will discuss some conjectures on Turan problems for bipartite graphs and some recent progress on them. Time permitting, we will also discuss a colored variant of the Turan problem.

There will also be a presentation on "Tao Jiang's favorite problems" (September 9, 11 - 11:50 a.m., Room 141 Altgeld Hall.