Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, April 6, 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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1  2  3  4  5  6                1  2  3                      1
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30 31

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.