Department of

# Mathematics

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

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
      April 2018              May 2018              June 2018
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3  4  5  6  7          1  2  3  4  5                   1  2
8  9 10 11 12 13 14    6  7  8  9 10 11 12    3  4  5  6  7  8  9
15 16 17 18 19 20 21   13 14 15 16 17 18 19   10 11 12 13 14 15 16
22 23 24 25 26 27 28   20 21 22 23 24 25 26   17 18 19 20 21 22 23
29 30                  27 28 29 30 31         24 25 26 27 28 29 30



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.