Department of

# Mathematics

Seminar Calendar
for events the day of Friday, September 8, 2017.

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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, September 8, 2017

12:00 pm in 243 Altgeld Hall,Friday, September 8, 2017

#### Life’s a blur, live on the edge

###### Derek Jung (UIUC)

Abstract: A focal problem in image processing is deblurring images and a common model for blurring images is convolution with a fixed kernel. I consider an integral operator arising from taking the blurred image of the edge of an opaque wall. I prove that the Tikhonov regularized problem for this operator is well-posed, which essentially means that one can invert the blurred image to the kernel continuously. This is joint work with Dr. Aaron Luttman and Dr. Kevin Joyce and was performed during a summer internship with National Security Technologies in Las Vegas. No background is necessary, but some knowledge of measure theory would be helpful.

1:00 pm in 141 Altgeld Hall,Friday, September 8, 2017

#### Keisler Measures, ctd.

###### Travis Nell   [email]

Abstract: We continue reading chapter 7 of Simon's A Guide to NIP Theories.

4:00 pm in 345 Altgeld Hall,Friday, September 8, 2017

#### "Borel circle squaring" by Marks and Unger: Part 1

###### Anton Bernshteyn (Illinois Math)

Abstract: This is the first in a series of talks based on a recent paper of A.S. Marks and S.T. Unger. In 1925, Tarski asked if it is possible to decompose a disk in the plane into finitely many pieces and then rearrange them to form a square of the same area. Due to the apparent similarity between this problem and the Banach--Tarski paradox, it might appear that any such "circle squaring" must rely on the Axiom of Choice; and indeed, in 1990 Laczkovich answered Tarski's question in the affirmative using a non-constructive approach. However, Marks and Unger show in their paper that, somewhat surprisingly, it is possible to perform a "circle squaring" using only Borel pieces. In this talk I will go over the history of the problem and sketch some of the main ingredients that go into Marks and Unger's proof.

4:00 pm in 241 Altgeld Hall,Friday, September 8, 2017

#### An Introduction to Classifying Spaces

###### Daniel Carmody (UIUC Math)

Abstract: In this introductory talk I'll begin by recalling the notion of a principal $G$-bundle, then I'll move to discussing how one constructs classifying spaces of such things. In the process, I'll introduce simplicial spaces and describe the relationship between simplicial spaces and topological spaces.