Department of

# Mathematics

Seminar Calendar
for events the day of Friday, February 15, 2019.

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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, February 15, 2019

2:00 pm in 141 Altgeld Hall,Friday, February 15, 2019

#### Convex geometry and the Mahler conjecture

###### Derek Kielty (Illinois Math)

Abstract: In this talk we will give an introduction to convex geometry and discuss the Mahler conjecture. This conjecture asserts that the product of the volume of a centrally symmetric convex set and the volume of its dual is minimized on a certain family of polytopes. We will also discuss a PDE analog of this conjecture.

3:00 pm in 341 Altgeld Hall ,Friday, February 15, 2019

#### Note the time and room change!"The complexity of topological group isomorphism" by A. Kechris, A. Nies, and K. Tent (Part 2)

###### Jenna Zomback (UIUC)

Abstract: This will be the second talk of the series on the paper in the title [arXiv link], which deals with the classification of some natural classes of non-Archimedean groups (= closed subgroups of S) up to topological group isomorphism. It gives a general criterion for a class of non-Archimedean groups to show that the topological group isomorphism on it is Borel-classifiable by countable structures. This criterion is satisfied by the classes of profinite groups, locally compact non-Archimedean groups, and oligomorphic groups. In this talk, we will fill in some proofs left out last time and prove this general criterion.

4:00 pm in Altgeld Hall 145 ,Friday, February 15, 2019

#### Laplacian Operator and Hyperbolic Geometry

###### Xiaolong Han (Illinois Math)

Abstract: The Laplacian operator acting on functions on a Riemannian manifold is an analytic operator invariant under isometry of the manifold. Its spectrum encodes much geometric information of the manifold. In this talk, I will start with some basic properties of Laplacian operator and hyperbolic geometry. Then I will talk about how these two interact with each other. Time permitting, I will talk about some of my recent works. No background on Laplacian operator or hyperbolic geometry is assumed.

4:00 pm in 241 Altgeld Hall,Friday, February 15, 2019

#### How to Give a Good Math Talk

###### uAWM, MATRIX, & IGL Outreach   [email] (UIUC Math)

Abstract: We will be having a workshop for undergraduates wishing to present and give a talk in the Undergraduate Seminar this semester (and in the future). We'll go through all the basics of giving an interesting talk as well as some details that can really make a presentation stand out.

4:00 pm in 245 Altgeld Hall,Friday, February 15, 2019

#### Harry Potter's Cloak Via Transformation Optics

###### Gunther Uhlmann (University of Washington)

Abstract: Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc. including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last fifteen years or so there have been several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion one of them, the so-called "transformation optics" which has received a lot of attention in the scientific community.