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

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