Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, November 8, 2016.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, November 8, 2016

1:00 pm in 241 Altgeld Hall,Tuesday, November 8, 2016

Heat content and horizontal mean curvature on†the Heisenberg group

Jing Wang (UIUC Math)

Abstract: In this talk we will discuss small time asymptotic expansion of the heat content on a domain of the Heisenberg group, which captures the geometric information including perimeter and horizontal mean curvature of the boundary of the domain. Our main tools are probabilistic method and Riemannian approximation. This is a joint work with J. Tyson.

1:00 pm in 345 Altgeld Hall,Tuesday, November 8, 2016

Time change equivalence of multidimensional Borel flows

Kostyantyn Slutskyy (UIC Math)

Abstract: A time change equivalence between free Borel $\mathbb{R}^n$-flows is defined to be an orbit equivalence which is also a homeomorphism when restricted onto any orbit. This notion appeared first in the set up of ergodic theory, when flows and orbit equivalence maps are required to preserve given probability measures, and all constructions are defined up to null sets. It is known that in this case there are continuumly many pairwise non equivalent ergodic $\mathbb{R}$-flows, but, surprisingly, Rudolph showed that any two free ergodic $\mathbb{R}^n$-flows, $n \ge 2$, are time change equivalent.
      In the context of Borel dynamics, Miller and Rosendal proved that all $\mathbb{R}$-flows are time change equivalent. They also posed a question of whether Rudolph's theorem is true in the Borel framework. We shall discuss a partial result in this direction, which shows that all free $\mathbb{R}^n$-flows are time change equivalent up to a compressible set.

1:00 pm in 7 Illini Hall,Tuesday, November 8, 2016

Decay Estimates for the 4D Schrodinger Equation

Ebru Toprak   [email] (UIUC Math)

Abstract: In this talk, I will present our latest improvement on the L^1 \rightarrow L^{\infty} dispersive estimate for the four dimensional Schrodingerís evolution when there is an obstruction at zero. I will introduce a technique in which we use oscillatory integral estimate methods and spectral properties of the Laplacian. I will explain what the obstructions at zero mean and how and why they effect the decay rate of the dispersive estimate.

2:00 pm in 241 Altgeld Hall,Tuesday, November 8, 2016

Langlands Correspondence and L-functions

Hao Sun (UIUC )

Abstract: I will talk about the langlands correspondence between Artin L-functions and the L-functions of automorphic representations.

3:00 pm in 241 Altgeld Hall,Tuesday, November 8, 2016

Two Counterexamples in Planar Graph Coloring

Xujun Liu (Illinois Math)

Abstract: The talk will have two parts. 1) A well-known Conjecture by Steinberg from 1976 states that every planar graph with no cycles of length four or five is $3$-colorable. We present a counterexample to this conjecture constructed by Cohen-Addad, Hebdige, Král, Li, and Salgado. 2) A $b$-fold coloring of a graph $G$ is a mapping $\phi$ which assigns to each vertex $v$ of $G$ a set $\phi(v)$ of $b$ colors so that adjacent vertices receive disjoint color sets. An $a$-list assignment of $G$ is a mapping $L$ which assigns to each vertex $v$ a set $L(v)$ of $a$ permissible colors. A $b$-fold $L$-coloring of $G$ is a $b$-fold coloring $\phi$ of $G$ such that $\phi(v) \subset L(v)$ for each vertex $v$. We say $G$ is $(a,b)$-choosable if for any $a$-list assignment $L$ of $G$, there is a $b$-fold $L$-coloring of $G$. Zhu proved recently that for each positive integer $m$, there is a planar graph $G$ which is not $(4m+\lfloor \frac{2m+1}{9} \rfloor,m)$-choosable. I will present his construction.

4:00 pm in 314 Altgeld Hall,Tuesday, November 8, 2016

Applications of Predictive Analytics: Improving Business Operations for Life Insurance Companies

Andy Ferris, FSA, MAAA, CFA (Managing Director at Deloitte Consulting)

Abstract: Why is the SOA adding a predictive analytics component to the ASA curriculum? Join Andy Ferris to hear about predictive analytics in practice. Ferris will discuss how his teams are deploying applications of predictive analytics to disrupt and improve core life insurance company operations. He'll present several examples of "traditional" business processes at life insurance companies and how those processes can be re-designed with applications of predictive analytics to save time, save money, and to deliver a better customer experience. He'll share his insights on the role of the actuary as "the engineer of a life insurance company" in introducing applications of predictive analytics in core business operations. Ferris will also explain how the changes in the ASA curriculum will ensure that all students going forward have a fundamental understanding of predictive analytics.

4:00 pm in 245 Altgeld Hall,Tuesday, November 8, 2016

Mathematics & Autonomy

Michael A. Warren (HRL Laboratories)

Abstract: Mathematical tools and techniques will have an important role to play in informing and guiding engineering and system design practice as it pertains to autonomous systems such as self-driving cars. Perhaps the most prominent interface between mathematics and autonomous systems research is via statistics and machine learning. However, this does not exhaust the usefulness of mathematics in this area. In this talk I will introduce some more exotic applications of mathematics ---drawing on a range of areas from logic to dynamical systems--- to autonomous and semi-autonomous systems.