Schedule

14:00-15:00	Claude Sabbah
15:15-16:15	Andrea D'Agnolo
coffee break
16:45-17:45	Teresa Monteiro Fernandes

Titles and Abstracts:

Claude Sabbah

Title: Hodge theory of Kloosterman connections
Abstract: Joint work with J. Fresán and J.-D. Yu. We construct motives over the rational numbers associated with symmetric power moments of Kloosterman sums, and prove that their L-functions extend meromorphically to the complex plane and satisfy a functional equation conjectured by Broadhurst and Roberts. Although the motives in question turn out to be "classica", the strategy consists in first realizing them as exponential motives and computing their Hodge numbers by means of the irregular Hodge filtration. We show that all Hodge numbers are either zero or one, which implies potential automorphy thanks to recent results of Patrikis and Taylor.

Andrea D'Agnolo

Title: Enhanced specialization and microlocalization
Abstract: In this talk I will illustrate a natural enhancement of Sato’s specialization
and microlocalization functors, suitable to deal with objects in
the target category of the irregular Riemann-Hilbert correspondence.
This is from joint works with Masaki Kashiwara.

Teresa Monteiro Fernandes

Title: Relative hermitian dual functor
Abstract: This talk aims to explain a recent joint work in progress with Claude Sabbah where we apply the relative Riemann-Hilbert correspondence recently proved by Luisa Fiorot, myself and Claude Sabbah to obtain a relative version of the so called conjugation functor (here denominated by dual hermitian functor) in the category of regular holonomic D-Modules by M. Kashiwara around 1986.
By construction this functor is an equivalence of categories, and, inspired by Kashiwara's method, we give an explicit construction.
We will treat a few interesting examples.