Department of

Mathematics

Seminar Calendar
for events the week of Saturday, April 10, 2021.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, April 5, 2021

3:00 pm in Zoom,Monday, April 5, 2021

Equivariant BPQ and Bicategorical Enrichment

Samuel Hsu (UIUC)

Abstract: Following the work of Guillou, May, Merling, and Osorno, we give a (very) broad overview of the (2-)algebraic input that goes into their proof of the multiplicative equivariant Barratt-Priddy-Quillen theorem. Although it is not explicitly invoked, an underlying point we wish to make is the presence of bicategorical enrichment over the 2-category of categories internal to G-spaces when G is a finite group, where bicategorical enrichment is meant in the sense of e.g. Garner--Shulman, Franco, or Lack. This also opens up a pathway to concepts like enriched analogues of bicategorical concepts, less celebrated structures such as double multi or poly categories, and other devices which are related to the usual celebrities in formal category theory, which we might discuss existing or hoped applications for, time permitting. This talk is intended to be accessible with hardly any knowledge of homotopy theory. Please email vb8 at illinois dot edu for the zoom details.

Tuesday, April 6, 2021

11:00 am in Zoom,Tuesday, April 6, 2021

A multiplicative theory of motivic infinite loop series

Brian Shin (UIUC)

Abstract: From a spectrum $E$ one can extract its infinite loop space $\Omega^\infty E = X$. The space $X$ comes with a rich structure. For example, since $X$ is a loop space, we know $\pi_0 X$ comes with a group structure. Better yet, since $X$ is a double loop space, we know $\pi_0 X$ is in fact an abelian group. How much structure does this space $X$ possess? In 1974 Segal gave the following answer to this question: the structure of an infinite loop space is exactly the structure of a grouplike $E_\infty$ monoid. In fact, this identification respects multiplicative structures. In this talk, I'd like to discuss the analogue of this story in the setting of motivic homotopy theory. In particular we'll see that the motivic story, while similar to the classical one, has a couple interesting twists.

For Zoom info, please email vesna@illinois.edu

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, April 6, 2021

Modified log-Sobolev inequalities, Beckner inequalities and moment estimates

Abstract: I will present recent results concerning the equivalence between the modified log-Sobolev inequality and a family of Beckner type inequalities with constants uniformly separated from zero. Next I will discuss moment estimates which can be derived from such inequalities, generalizing previous results due to Aida and Stroock, based on a stronger log-Sobolev inequality due to Federbush and Gross. If time permits I will present examples to moment estimates for certain Cauchy type measures, for invariant measures of Glauber dynamics and on the Poisson path space. Based on joint work with B. Polaczyk and M. Strzelecki.

2:00 pm in Zoom,Tuesday, April 6, 2021

Size of Sidon sets revisited

Jozsef Balogh (UIUC)

Abstract: Earlier in this semester, Zoltan Furedi gave a talk, where he presented a proof for the best known upper bound on sizes of Sidon subsets of $\{1,\dots,n\}$. In this talk we repeat his proof, and explore the differences from other proofs of the same bound.

The talk is based on discussions with Zoltan Furedi and Souktik Roy.

Thursday, April 8, 2021

11:00 am in zoom,Thursday, April 8, 2021

Deformations of symplectic foliations

Marco Zambon (KU Leuven)

Abstract: Symplectic foliations and regular Poisson structures are the same thing. Taking the latter point of view, we exhibit an algebraic structure that governs the deformations of symplectic foliations, i.e. which allows to describe the space of symplectic foliations nearby a given one. Using this, we will address the question of when it is possible to prolong a first order deformation to a smooth path of symplectic foliations. We will be especially interested in the relation to the underlying foliation. This is joint work in progress with Stephane Geudens and Alfonso Tortorella.

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

Friday, April 9, 2021

4:00 pm in Zoom,Friday, April 9, 2021

The Yamabe Problem

Xinran Yu (UIUC)

Abstract: In a two-dimensional case, the fact that every Riemann surface has a metric with constant Gaussian curvature leads to a successful classification of Riemann surfaces. Generalizing this property to higher dimensions could be an interesting problem to consider. Thus we seek a conformal metric on a compact Riemannian manifold with constant scalar curvature. The Yamabe problem was solved in the 1980s, due to Yamabe, Trudinger, Aubin, and Schoen. Their solution to the Yamabe problem uses the techniques of calculus of variation and elliptic regularity of the Laplacian. The proof introduces a conformal invariant, so-called the Yamabe invariant, which shifts the focus from an analysis point of view to understanding a geometric invariant. The solution is separated nicely into two cases, regarding the dimension and flatness of a given Riemannian manifold. For Zoom details, please email basilio3 (at) illinois (dot) edu.

4:00 pm in Zoom,Friday, April 9, 2021

To Be Announced

Prof. Reuven Hodges   [email] (UIUC Math)

Abstract: TBA

4:30 pm in Zoom,Friday, April 9, 2021