Department of

Mathematics


Seminar Calendar
for Colloquium events the year of Friday, January 1, 2021.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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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.

For Zoom info, please contact jobal@illinois.edu

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.

For Zoom info, please contact jobal@illinois.edu

Thursday, April 8, 2021

3:00 pm in Zoom,Thursday, April 8, 2021

Recent advances in analysis of implicit bias of gradient descent on deep networks

Matus Telgarsky (UIUC)

Abstract: The purpose of this talk is to highlight three recent directions in the study of implicit bias, a promising approach to developing a tight generalization theory for deep networks interwoven with optimization. The first direction is a warm-up with purely linear predictors: here, the implicit bias perspective gives the fastest known hard-margin SVM solver! The second direction is on the early training phase with shallow networks: here, implicit bias leads to good training and testing error, with not just narrow networks but also arbitrarily large ones. The talk concludes with deep networks, providing a variety of structural lemmas that capture foundational aspects of how weights evolve for any width and sufficiently large amounts of training. This is joint work with Ziwei Ji.

To register: https://berkeley.zoom.us/webinar/register/WN_iEXcldw1QPOuUofhS0WT4g

Tuesday, April 13, 2021

12:30 pm in Zoom,Tuesday, April 13, 2021

Poverty and Pandemic: Tackling current issues using actuarial methodologies

Dr. Sooie-Hoe Loke, assistant professor (Central Washington University)

Abstract: Traditionally, actuarial science involves quantifying risks in the insurance and finance industry. Its scope has broadened tremendously since its introduction as a formal mathematical discipline in the 17th century. In this talk, we discuss several applications, particularly to some current issues in our society today, such as poverty and pandemic. Questions welcomed at the end. Join the meeting at: https://illinois.zoom.us/j/87086696430?pwd=aHFaeGV0Z29PUGdpVWlDMTlzM3BoZz09.

Thursday, April 15, 2021

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

Flat Littlewood polynomials exist

Robert Morris (IMPA, Brazil)

Abstract: Click here for abstract

For Zoom info, please contact jobal@illinois.edu

Monday, April 19, 2021

1:00 pm in via Zoom,Monday, April 19, 2021

Metamodeling for variable annuity valuation: What works and what does not

Xiaochen Jing   [email] (University of Wisconsin, Madison)

Abstract: Variable Annuities have become popular retirement products with various options of guarantees, but their complex design also makes liability management a difficult task for insurers. There have been several dozen papers published in the past years on exploring the use of statistical learning and metamodeling approaches for Variable Annuity valuation and risk management in the actuarial science and quantitative finance literatures. However, they all focus on specific techniques in the context of synthetic data. In this paper, I investigate the effectiveness of metamodeling approaches with different experimental designs and metamodels with real-world Variable Annuity contracts. In particular, I use textual analysis to extract and formulate value-related features and develop a flexible and comprehensive simulation-based scheme for Variable Annuity valuation. I find that (1) real-world variable annuity contracts are very complex and the intricate relations between their valuation and features are difficult to obtain. And (2) the overall performance of a metamodeling method depends on the employed machine learning methods as well as the sample size---though not substantially on the sampling methods. Both improve performance at the cost of longer runtime.

For Zoom info, please contact wfchong@illinois.edu

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.