Jesse Thorner (University of Illinois) – An approximate form of Artin’s holomorphy conjecture and nonvanishing of Artin L-functions.

I will present some recent work with Robert Lemke Oliver
and Asif Zaman in which we noticeably expand the region in which
almost all Artin L-functions in certain families are holomorphic and
nonvanishing.  This combines Galois theory, character theory, and
analytic number theory.  These results are motivated by a wide range
of classically flavored applications; I will focus on applications to
the study of class groups of high-degree number fields.

Joshua Males (University of Cologne) – Cycle integrals, theta lifts, and modular forms.

Cycle integrals are intricately linked to many areas of maths. For example, they encode special values of L-functions, give loop amplitudes in string theory, and appear in algebraic geometry. They can often be realised as certain theta lifts. In this talk I’ll give an overview of recent developments in the use of generalised modular forms in determining rationality results of such cycle integrals. Inspired by breakthrough works of Bringmann-Kane-Kohnen and Bruinier-Ehlen-Yang, I will describe some new results on a certain theta lift, and its relationship to cycle integrals, and how it can be realised in terms of coefficients of generalised modular forms. For example, we see how one can recover relationships to Hurwitz class numbers, or the classical spt partition function.

I will also briefly discuss some related ongoing and future topics. Parts of this talk are based on work with Alfes-Neumann, Bringmann, and Schwagenscheidt as well as Scharf and Schwagenscheidt.

Kathrin Bringmann (University of Cologne) – False theta functions and their modularity properties.

In my talk I will explain how to embed false theta functions into a modular framework and discuss applications.

Wei-Lun Tsai (University of Virginia) – TBA

TBA.

Soon-Yi Kang (Kangwon National University) – TBA

TBA.