Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, October 27, 2020.

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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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Tuesday, October 27, 2020

11:00 am in via Zoom (email vesna@illinois.edu for link),Tuesday, October 27, 2020

#### Decomposition of topological Azumaya algebras

###### Niny Arcila Maya (University of British Columbia)

Abstract: Let $\mathcal{A}$ be a topological Azumaya algebra of degree $mn$ over a CW complex $X$. We give conditions for the positive integers $m$ and $n$, and the space $X$ so that $\mathcal{A}$ can be decomposed as the tensor product of topological Azumaya algebras of degrees $m$ and $n$. Then we prove that if $m$<$n$ and the dimension of $X$ is higher than $2m+1$, $\mathcal{A}$ has no such decomposition. Please email vesna@illinois.edu for Zoom link.

11:00 am in Zoom,Tuesday, October 27, 2020

#### Distribution of reduced quadratic irrationals arising from even and of backward CF expansions

###### Maria Siskaki (UIUC Math)

Abstract: : The reduced quadratic irrationals (RQIs) coming from the regular continued Fraction (CF) expansion, when ordered by their length, are known to be uniformly distributed with respect to the Gauss probability measure. In this talk I will present the corresponding result for the RQIs arising from the even and backwards CF expansions, where the invariant measure is infinite. I will also be mentioning their connection with the Pell equation. This is joint work with F. Boca.

2:00 pm in Zoom,Tuesday, October 27, 2020

#### Universality of random polynomials

###### Oanh Nguyen (UIUC)

Abstract: Consider polynomials whose coefficients are 1 or -1. How many real roots do such polynomials typically have? This is one of the basic questions that we study in the field of random polynomials. In this talk, we will discuss the history and recent progress in the field. We will also discuss several current lines of research and intriguing open problems.

Contact Sean at SEnglish (at) illinois (dot) edu for Zoom information.

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, October 27, 2020

#### Quantitative quenched CLTs for one-dimensional random walks in random environments

###### Jonathon Peterson (Purdue University)

Abstract: The Berry-Esseen estimates give quantitative error estimates on the CLT for sums of i.i.d. random variables, and the polynomial decay rate for the error depends on moment bounds of the i.i.d. random variables with the optimal $1/\sqrt{n}$ rate of convergence obtained under a third moment assumption. In this talk we will prove quantitative error bounds for quenched CLTs of both the position and hitting times of one dimensional random walks in random environments (RWRE). For the quantitative CLTs for the hitting times we prove that our rates our optimal. This talk is based on joint works with Sungwon Ahn.

8:00 pm in via Zoom (please email wfchong@illinois.edu),Tuesday, October 27, 2020