Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, March 5, 2019.

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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, March 5, 2019

1:00 pm in 347 Altgeld Hall,Tuesday, March 5, 2019

#### Some recent progress on the Falconer distance conjecture and applications

###### Alex Iosevich (U. Rochester)

Abstract: We are going to discuss some recent results related to the Falconer distance conjecture and applications of some of these methods to the theory of exponential bases and frames.

1:00 pm in 345 Altgeld Hall,Tuesday, March 5, 2019

#### Descriptive graph combinatorics with applications to geometry

###### Spencer Unger (Tel Aviv University)

Abstract: The Banach–Tarski paradox states that (assuming the axiom of choice) a unit ball in $\mathbb{R}^3$ can be partitioned into $5$ sets which can be rearranged by isometries to partition two unit balls. This famous result is part of a larger line of early 20th century research which sought to understand the relation between foundations of measure theory and generalizations of classical ideas such as decomposing polygons into congruent sets.
In the last few years, there has been a resurgence of interest in these geometrical paradoxes. These results have the unifying theme that the "paradoxical" sets in many classical geometrical paradoxes can surprisingly be much "nicer" than one would naively expect. In this talk, we give a survey of these results and explain a few of the ideas that go in to a constructive solution to Tarski's circle squaring problem. This is joint work with Andrew Marks.

2:00 pm in 243 Altgeld Hall,Tuesday, March 5, 2019

#### Polynomial to exponential transition in hypergraph Ramsey theory

###### Lina Li (Illinois Math)

Abstract: Let $r_k(s, t; n)$ be the minimum $N$ such that every red/blue colorings of the edges of $K^k_N$ contains a blue $K^k_n$ or has $s$ vertices which induce at least $t$ red edges. The study of $r_k(s, t; n)$ is related to many other classical problems, such as classical Ramsey theory and Erdős–Szekeres problem.

The main problem of Erdős and Hajnal asks for the growth rate of $r_k(s, t; n)$ when $t$ changes from $1$ to $s \choose k$. In particular, they conjectured that for given $s$ and $k$, the threshold of $t$ which separates the polynomial growth rate and super polynomial growth rate can be calculated precisely by a recursive formula.

In this talk, I will present the history of this problem, and discuss the most recent progress made by Mubayi and Razborov, who resolve the above conjecture.

3:00 pm in 243 Altgeld Hall,Tuesday, March 5, 2019

#### Modeling Learning and Strategy Formation in Phase Transitions in Cortical Networks

###### Kesav Krishnan (University of Illinois at Urbana–Champaign)

Abstract: In the first of 2 seminars on this paper by Kozma++ we review the experimental data and their graph-theoretic methods. In the second, we review the mathematical details and offer a critique of their results. Here is a paraphrase of the authors abstract: Learning in mammalian brains is commonly modeled in terms of synaptic connections in a cortical network and the formation of limit cycle oscillators of a dynamical system. Learning is inferred by the re-emergence of the oscillatory regimes by repeating the stimulus. Here the authors use random graphs and boostrap percolation with excitatory and ihibitory vertices. The phase transition from fixed point attractors to limit cycles (Hopf bifurcations) represent changes in cortical networks during category learning. A correspondence with analogous event in the gerbil cortex is based on experiments with electro-cortiographs (ECoG) arrays. They discuss how learning leads to categorization and strategy formation, and how the theoretical modeling results can be used for designing learning and adaptation in computationally aware intelligent machines.

4:00 pm in 245 Altgeld Hall,Tuesday, March 5, 2019

#### Altgeld-Illini Renovation/Building Project Feedback Session

Abstract: CANCELED

6:30 pm in 1320 Digital Computer Lab,Tuesday, March 5, 2019

#### Introduction to CAS, Ratemaking, and Emerging Insure Tech Trends

###### Steve Armstrong (Allstate; President-elect, the Casualty Actuarial Society)

Abstract: Steve Armstrong is a personal insurance expert with over 25 years of extensive experience in pricing, product design, underwriting, and regulatory work. Throughout this career, Steve has led teams of actuaries, predictive modelers, and product analysts; he has also served as an expert witness in several states. Steve began his career at Allstate Insurance Company, where he worked as an actuary overseeing actuarial and analytical talent for auto and homeowners insurance focusing on both the state-specific rate reviews and filings and the predictive modeling and countrywide rating plan development. During his tenure, Steve was responsible for introducing the product and rating algorithm for Drivewise, Allstate’s usage-based insurance endeavor before he left in 2012. Between 2012 and 2017, Steve worked for two large global insurance companies to help bring actuarial best practices to these companies and to other countries ar ound the world. Steve recently returned to Allstate to oversee actuarial work and lead actuarial pricing strategy for private passenger automobile. Steve received his Bachelor of Science degree in Actuarial Science from the University of Illinois – Urbana-Champaign in 1992 and his MBA from the University of Illinois – Chicago in 2003. Steve received his Casualty Actuarial Society (CAS) Fellowship in 1996; he served on the CAS Board of Directors from 2011- 2014 and as the CAS Vice President of Admissions from 2014-2017.