Department of

Mathematics


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

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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

Cyber: How risky is it, really?

Chad Spensky (Founder and CEO, Allthenticate)

Abstract: The news is filled with articles about data breaches and mindbending hacks. Similarly, cybersecurity defenses, many of which are quite expensive, are touted as necessary for any business these days, as is cybersecurity insurance. Yet, it is frequently unclear how big of risk companies are actually facing. More precisely, what is the likelihood that your company will be targeted by a cyber attack? If it is, and they are successful, how much financial damage can they do? Or, maybe you are wondering the more obvious question, "what is a cyber-attack?" Throughout my career, I have been a blackhat hacker, a cybersecurity researcher, and am now the CEO of a security company. Wearing these various hats has given me a unique insight into this field and the problems that face modern businesses and individuals. In this talk, I will first explain what a cyber attack is, and then attempt to quantify how difficult (and thus likely) specific attacks are. The goal of this talk is to provide the necessary technical background to anyone that is thinking about the higher-level cyber questions (e.g., "Should I buy cyber insurance?" or "How likely is it that an attack can dump our customer database?"), and provide them with the knowledge required to reason about this growing threat in a rational, informed way. Chad Spensky is a computer security researcher, entrepreneur, and educator who is passionate about using technology to make people’s lives easier and their digital systems more secure. Chad has over 10 years of research experience and is a lifetime hacker. Formerly, he was a member of the technical research staff at MIT Lincoln Laboratory, where he helped them solve some of the Department of Defense's toughest cyber-security problems. Chad received his Ph.D. from the University of California, Santa Barbara in 2020 and is also a recipient of the prestigious IBM PhD Fellowship. As a hacker and capture the flag player himself, he is well aware of how attackers think and believes that it takes a great offense to build a solid defense. Zoom link: please email wfchong@illinois.edu