Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, September 26, 2018.

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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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Wednesday, September 26, 2018

3:00 pm in 241 Altgeld Hall,Wednesday, September 26, 2018

#### A combinatorial proof of the classical pointwise ergodic theorem

###### Jenna Zomback (UIUC Math)

Abstract: We will discuss A. Tserunyan's proof of the classical pointwise ergodic theorem for pmp actions of $\mathbb{Z}$ given in [arXiv link], which reduces proving this analytic theorem to solving a finitary tiling problem on the Cayley graph of $\mathbb{Z}$. We hope to use this method in the future to give streamlined proofs of known instances of the pointwise ergodic theorem for other groups, as well as obtain new ones.

4:00 pm in 2 Illini Hall,Wednesday, September 26, 2018

#### Line bundles on abelian varieties

###### Matej Penciak   [email] (UIUC Math)

Abstract: In this talk I want to give classical results on line bundles on abelian varieties. I’ll begin with the Appel-Humbert theorem. Then I will give an introduction to theta functions and show that they can be identified with sections of line bundles. This will connect the older approach with the more well-known description in terms of divisors. Finally, I’ll consider more general problem of classifying vector bundles on elliptic curves, and describe Atiyah’s solution to the classification problem.