Events

In this talk, we describe a construction of closed 4-manifolds with finite fundamental group and the rational homology of RP^4. These new families of 4-manifolds include non-smoothable examples and inequivalent smooth structures. Joint work with Valentina Bais. 

(Joint work with T. Untrau) Many equidistribution theorems in number theory are proved by means
of the Weyl Criterion and quantitative bounds for $L$-functions or related quantities. It is natural to
want to translate these statements into quantitative equidistribution results in terms of distances
between probability measures. Wasserstein metrics provide an intrinsic and highly flexible framework
for such statements. The talk will survey the underlying definitions and give examples of applications,

Reciprocity in the context of $L$-functions refers to a relation between
a moment of $L$-functions and a dual moment in a way that swaps
the roles of certain key parameters on both sides. In this talk I will discuss
reciprocity for the first moment of $GL(2)$ $L$-functions twisted by Dirichlet
characters.

We pin down the function $\phi$ of minimal $L^1$ norm among all functions $f$
of exponential type at most $\pi$ for which $f(0)=1$. The problem of describing
$\phi$ has surfaced in many different contexts during the past 35 years, including
analytic number theory and the study of prime gaps. Our work is inspired by a
remarkable 1993 paper of Hörmander and Bernhardsson. The talk is based on joint
work with Andriy Bondarenko, Joaquim Ortega-Cerdá, and Danylo Radchenko.