# Events for 12/05/2023 from all calendars

## Number Theory Seminar

**Time: ** 11:10AM - 12:10PM

**Location: ** BLOC 302

**Speaker: **Giacomo Ferraro, Sapienza University of Rome

**Title: ***A rationality result regarding Pellarin L-functions and special functions*

**Abstract: **The theory of Drinfeld modules, pioneered by Anderson and Thakur in the 90’s, was conceived as a possible analogue to the theory of complex elliptic curves in finite characteristic, where the role of the ring of integers is assumed by the ring of regular functions of some curve $X/\mathbb{F}_q$ outside a point $\infty\in X$. We will introduce Gauss-Thakur sums and Pellarin L-values as analogues to Gauss sums and Dirichlet L-values respectively.
Two novel objects – special functions and Pellarin L-functions – arise in this theory, which have no analogue in characteristic 0: they interpolate respectively Gauss-Thakur sums and Pellarin L-values over all possible characters.
The main theorem we will talk about is the rationality of the product of special functions and Pellarin L-functions, highlighting its similarity to the classical functional equation for Dirichlet L-functions.

## Nonlinear Partial Differential Equations

**Time: ** 3:00PM - 4:00PM

**Location: ** BLOC 302

**Speaker: **Maxime van de Mortel, Rutgers University

**Title: ***Asymptotic behavior of the Klein-Gordon equation on a Schwarzschild black hole*

**Abstract: **It has long been conjectured that the Klein-Gordon equation on a Schwarzschild black hole behaves very differently from the wave equation at late-times, and only decays at a slow t^{-5/6} rate. Despite its apparent simplicity, this conjecture had remained open. We discuss its resolution and our recent result establishing late-time tails at the rate t^{-5/6} for each angular mode.
Joint work with Federico Pasqualotto and Yakov Shlapentokh-Rothman.

## Colloquium

**Time: ** 4:00PM - 5:00PM

**Location: ** BLOC 117

**Speaker: **Hoi Nguyen

**Description: **Title: On roots of random polynomials
Abstract: The study of roots of random polynomials is an active area of research that has been ongoing since the early 1900s. In this talk we will discuss some recent developments, focusing on robust frameworks to establish universality. These include the global and local correlation of roots, the variance of the number of real roots, concentration phenomen, and CLT fluctuation.