Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, May 1, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, May 1, 2018

11:00 am in 241 Altgeld Hall,Tuesday, May 1, 2018

Average non-vanishing of Dirichlet L-functions at the central point

Kyle Pratt (Illinois Math)

Abstract: One expects that an L-function vanishes at the central point either for either deep arithmetic reasons, or for trivial reasons. The central values of Dirichlet L-functions have no arithmetic content, and are also not forced to vanish by the functional equation. One is then led to believe that these central values never vanish, which is a conjecture going back in one form or other to Chowla. The Generalized Riemann Hypothesis implies that almost half of these central values are nonzero. In this talk I will discuss my recent work on central values of Dirichlet L-functions. The main theorem, an unconditional result, is beyond the reach of the Generalized Riemann Hypothesis.

11:00 am in 345 Altgeld Hall,Tuesday, May 1, 2018

Motivic homotopical Galois extensions

(UIUC)

Abstract: TBA

12:00 pm in 243 Altgeld Hall,Tuesday, May 1, 2018

Polygonal billiards, Liouville currents, and rigidity

Chris Leininger (Illinois Math)

Abstract: A particle bouncing around inside a Euclidean polygon gives rise to a biinfinite "bounce sequence" (or "cutting sequence") recording the (labeled) sides encountered by the particle. In this talk, I will describe recent work with Duchin, Erlandsson, and Sadanand, where we prove that the set of all bounce sequences---the "bounce spectrum"---essentially determines the shape of the polygon. This is consequence of a technical result about Liouville currents associated to nonpositively curved Euclidean cone metrics on surfaces. In the talk I will explain the objects mentioned above, how they relate to each other, and give some idea of how one determines the shape of the polygon from its bounce spectrum.

2:00 pm in 347 Altgeld Hall,Tuesday, May 1, 2018

On the potential theory of subordinate killed processes

Zoran Vondraček (University of Zagreb)

Abstract: Let $Z$ be an isotropic stable process in the Euclidean space. The process $Z$ is killed upon exiting an open set $D$ and the killed process is then subordinated by an independent $\gamma$-stable subordinator, $0<\gamma <1$. The resulting process is a Hunt process in $D$. In this talk, I will discuss several potential theoretical properties of this process such as Harnack inequality for nonnegative harmonic functions, the Carleson estimate, Green function and jumping kernel estimates in smooth sets $D$, and in particular, the boundary Harnack principle. Surprisingly, it turns out the BHP holds only if $1/2<\gamma<1$. This is joint work with Panki Kim and Renming Song.

3:00 pm in 241 Altgeld Hall,Tuesday, May 1, 2018

Planar graphs without adjacent cycles of length at most 8 are 3-choosable

Xiangwen Li (Central China Normal University, Math)

Abstract: DP-coloring as a generation of list coloring was introduced by Dvořák and Postle in 2017, who proved that every planar graph without cycles from 4 to 8 is 3-choosable, which was conjectured by Brodian et al. in 2007. In this paper, we prove that planar graphs without adjacent cycles of length at most 8 are 3-choosable, which extends this result of Dvořák and Postle.