Department of

Mathematics


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

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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.

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.