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.

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.