Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 6, 2020.

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events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, November 6, 2020

1:00 pm in Zoom,Friday, November 6, 2020

#### Maximization of the second Laplacian Eigenvalue on the sphere

###### Hanna Kim (UIUC Math)

Abstract: I will explain a simplified approach to proving that the upper bound of the second (nonzero) eigenvalue of the Laplacian operator on the sphere can be maximized by considering a sequence of metrics. This sequence of metrics is going to that of 2-disjoint spheres with the same size. We construct trial functions using energy minimization which goes back to Szeg\"{o} and Weinberger.

3:00 pm in Zoom,Friday, November 6, 2020

#### Gender, Sexuality and Math

###### Bianca Thompson (Westminster College)

Abstract: Are you interested in learning about gender, sexuality and its intersection with mathematics? Then this seminar is for you! The Teaching and Diversity Seminar is excited to have Dr. Bianca Thompson who will provide us with the framework to think about gender, sexuality, and its intersection with our mathematical identity. The goal is to think more about what a Queer Mathematical environment could be. Based on reading or personal experience we want to have a discussion on the barriers that persist in mathematics preventing participation from LGBTQAIP+ community members and how can we remove those barriers. Email na17 [AT] illinois [DOT] edu for the Zoom details.

4:00 pm in Zoom (email ruiyuan at illinois for info),Friday, November 6, 2020

#### The fractal properties of real sets defined by Büchi automata

###### Christian Schulz (UIUC Math)

Abstract: Büchi automata are a natural counterpart to finite automata that accept infinite strings instead of finite strings as input. We consider the k-automatic sets, which are subsets of $[0, 1]^n$ consisting of all tuples with a base-k expansion recognized by a given Büchi automaton. These sets often exhibit fractal behavior; for instance, the Cantor set and Sierpinski carpet are both 3-automatic. In this talk, we give methods for measuring various fractal properties of a k-automatic set, including box-counting dimension and Hausdorff dimension and measure, by examining the structure of its Büchi automaton. This is joint work with Alexi Block Gorman and Philipp Hieronymi.