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Seminar Calendar
for events the day of Friday, September 6, 2019.

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Friday, September 6, 2019

2:00 pm in 347 Altgeld Hall,Friday, September 6, 2019

Quantum Symmetry in the context of co/representation categories

Chelsea Walton (UIUC)

Abstract: In the first 50 minutes, I will provide an introductory talk on quantum symmetry in the context of co/representation categories, which serves as one point of motivation for the reading group on Tensor Categories. I will then give a follow-up research talk in the second 50 minutes on joint work in progress with Elizabeth Wicks and Robert Won on quantum symmetry and weak Hopf algebras.

3:00 pm in 341 Altgeld Hall,Friday, September 6, 2019

Introduction to Metric Embeddings into Banach Spaces

Chris Gartland (UIUC)

Abstract: This talk will survey some results on the existence or nonexistence of embeddings of certain metric spaces into Banach spaces. Some proofs will be provided whenever sufficiently elementary, but most results will only be stated. There is a wealth of tools used in this field, and we'll encounter results whose proofs could include graph-theoretical combinatorics or abstract harmonic analysis. Topics to be covered (time permitting of course) range from: elementary facts - every finite metric space isometrically embeds into $\ell^\infty$, to graduate level analysis - almost everywhere differentiation of absolutely continuous functions, and finally to a recent, deep application in computer science - a full solution to the Goemans-Linial conjecture. Families of expander graphs and the Heisenberg group are metric spaces that play a special role in this story.

3:00 pm in Illini Hall 1,Friday, September 6, 2019

Series and Polytopes

Vivek Kaushik (Illinois Math)

Abstract: Consider the series $S(k)=\sum_{n \geq 0} \frac{(-1)^{nk}}{(2n+1)^k}$ for $k \in \mathbb{N}.$ It is well-known that $S(k)$ is a rational multiple of $\pi^k$ using standard techniques from either Fourier Analysis or Complex Variables. But in this talk, we evaluate $S(k)$ through multiple integration. On one hand, we start with a $k$-dimensional integral that is equal to the series in question. On the other hand, a trigonometric change of variables shows the series is equal to the volume of a convex polytope in $\mathbb{R}^k.$ This volume is proportional to a probability involving certain pairwise sums of $k$ independent uniform random variables on $(0,1).$ We obtain this probability using combinatorial analysis and multiple integration, which ultimately leads to us finding an alternative, novel closed formula of $S(k).$

4:00 pm in 345 Altgeld Hall,Friday, September 6, 2019

"On the nonexistence of Følner sets" by Isaac Goldbring

Elliot Kaplan (UIUC Math)

Abstract: This will be the first (and possibly only) talk on the preprint "On the nonexistence of Følner sets" by Isaac Goldbring ( I will introduce all of the necessary model-theoretic and group-theoretic background. Time permitting, I may get to the proof of the main result.

4:00 pm in 141 Altgeld Hall,Friday, September 6, 2019

Geometry by example: the projective plane

Nachiketa Adhikari (UIUC)

Abstract: In this expository talk, I will introduce the projective plane, and use it to explore a range of ideas including moment polytopes, localization formulas and intersection theory.