Department of

Mathematics


Seminar Calendar
for events the day of Thursday, September 11, 2014.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, September 11, 2014

10:00 am in 143 Altgeld Hall,Thursday, September 11, 2014

A Definition of Quasiconformality Involving Only Squares

Colleen Ackermann (UIUC Math)

Abstract: The geometric definition of quasiconformal mappings is a statement involving all quadrilaterals. Over the years it has been shown that instead of considering all quadrilaterals, it suffices to consider various subsets of quadrilaterals. I will discuss the open question of whether or not it suffices to only consider squares. This talk will be at a level accessible to all graduate students.

11:00 am in 241 Altgeld Hall,Thursday, September 11, 2014

Mahler measures, special $L$-values, and elliptic polylogarithms

Detchat Samart   [email] (UIUC Math)

Abstract: The Mahler measure of an $n$-variable Laurent polynomial $P$ is defined to be the arithmetic mean of $\log |P|$ over the $n$-torus. In certain cases, Mahler measures are known to be expressible in terms of special values of $L$-functions. In this talk, we will present some results and conjectures relating Mahler measures of polynomials defining elliptic curves and $K3$ surfaces to non-critical modular $L$-values. We shall also define elliptic polylogarithm functions and give some general Mahler measure formulas in terms of these functions.

2:00 pm in 347 Altgeld Hall,Thursday, September 11, 2014

Dynamical systems perturbed by Levy noise

Ilya Pavlyukevich (University of Jena Math)

Abstract: In this talk we address two peculiarities which may appear when one deals with perturbations of dynamical systems by Levy noise. First we discuss the differences between multiplicative noises in the sense of Ito, Stratonovich and Marcus integration. Second, we consider the first exit problem for a charged Levy particle in an external magnetic field in the context of non-standard Skorohod convergence.

2:00 pm in 241 Altgeld Hall,Thursday, September 11, 2014

Shellability- A Combinatorial Tool with Topological Implications

Amelia Tebbe (University of Illinois at Urbana-Champaign)

Abstract: I plan to give an introduction to shellability, which is a property of simplicial complexes and partially ordered sets. I will discuss a nice homotopy consequence of shellability and sketch the proof. If time allows, I will talk about how this topic fits into the larger picture of my research.

2:00 pm in 007 Illini Hall,Thursday, September 11, 2014

Moments of the average of a generalized Ramanujan sum

Nicolas Robles (University of Zurich, Switzerland)

Abstract: The moments of the average of a generalized Ramanujan sums are derived. This generalization was introduced by Cohen. We will also obtained some improvements of some previous results on the moments of the average of the Ramanujan sums. Related explicit formulae involving the non-trivial zeros of the Riemann zeta-function are also derived. This is joint work with Arindam Roy.

4:00 pm in 245 Altgeld Hall,Thursday, September 11, 2014

Transitivity degrees of infinite groups

Denis Osin (Vanderbilt)

Abstract: I will talk about my work in progress with Michael Hull. Given a group $G$ we define its transitivity degree, denoted $td(G)$, as the supremum of all $k$ such that $G$ admits a $k$-transitive action on a set with at least $k$ elements. This notion is classical in the context of finite groups. I will survey recent results on transitivity degrees of infinite groups. In particular, I will discuss the following phenomenon: in various algebraic and geometric settings (e.g., for subgroups of mapping class groups, $3$-manifold groups, etc.) $td(G)$ can only take two values, namely $1$ and $\infty$, and groups with $td(G)=\infty$ can be characterized by the existence of a certain action on a hyperbolic space.