Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 12, 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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Friday, November 12, 2021

2:00 pm in 347 Altgeld Hall,Friday, November 12, 2021

#### Functional & Geometric Inequalities: An Introduction

###### Rachel Barnett (UIUC)

Abstract: Abstract: This talk introduces functional and geometric inequalities, opening with a discussion about what they are and key questions that frame their study. We prove the Polya-Szego inequality and then use it to establish the classical Faber-Krahn inequality, which states that balls minimize the first eigenvalue of the Dirichlet Laplacian among all sets of the same volume. We conclude by outlining what a more general Faber-Krahn inequality looks like and how one might go about deriving it. This talk is based on a paper by Brasco and De Phillips (2016).

3:00 pm in 243 Altgeld Hall,Friday, November 12, 2021

#### ∞-categorical Kummer theory

###### Abhra Kundu (UIUC Math)

Abstract: Kummer theory provides a way of recognizing the isomorphism classes of (certain) Galois extensions of fields containing enough roots of unity. Running a similar machinery for general classical commutative rings leads to the classification of (certain) Galois extensions of the ring which involves the Picard spectrum of the ring. Schlank, et al. have designed a version of this theory that works for nice presentable additive symmetric monoidal ∞-categories which involves the Picard spectrum of this category. I will go over their version of the theory in this talk.