Luxembourg Number Theory Day 2024
The Luxembourg Number Theory Day will take place on December 18, 2024, on the Esch-Belval Campus of the University of Luxembourg. The talks will be held in room MNO 1.030 of the Maison du Nombre. Everyone is invited to attend!
Contact and Registration
Registration is open (in person and online)! For more information and to register for the Luxembourg Number Theory Day 2024, please write to the organiser Félix Baril Boudreau at felix PERIOD barilboudreau AT uni DOT lu.Speakers
Anne-Marie Aubert (Sorbonne Université and Université Paris Cité)Jayce Getz (Duke University)
Alfio Fabio LA ROSA (University of Luxembourg)
Qing Liu (Université de Bordeaux)
Location
All of the talks will take place in room MNO 1.030 on the 1st floor of the Maison du Nombre at 6, Avenue de la Fonte, Esch-sur Alzette. You can find it on Google Maps or OpenStreetMap.Schedule
9:15 Qing Liu (Université de Bordeaux)
10:15 Jayce Getz (Duke University)
11:30 Anne-Marie Aubert (Sorbonne Université and Université Paris Cité)
14:15 Alfio Fabio La Rosa (University of Luxembourg) [PhD Defence]
Abstracts
Anne-Marie Aubert (Sorbonne Université and Université Paris Cité) Stable blocks and enhanced Langlands parameters
The decomposition into Bernstein blocks of the category of smooth representations of a p-adic group G admits a Galois analogue in terms of enhanced L-parameters, in which the role of supercuspidal representations is played by "cuspidal" enhanced L-parameters, a notion that originates in the construction by Lusztig of the generalized Springer correspondence.
We will formulate sufficient conditions to be satisfied by the local Langlands correspondence for the supercuspidal representations of the Levi subgroups of G in order to allow to construct a canonical bijection between the associated blocks on both sides.
Next, when these conditions are satisfied, we will explain how to gather these blocks together into bigger ones that are unions of L-packets.
Jayce Getz (Duke University) Triple product L-functions: first reduction
I will describe a period integral that unfolds to the triple product L-function times L-functions whose analytic properties are understood. Motivated by the period integral, I will then formulate an extension of the Poisson summation conjecture of Braverman-Kazhdan, L. Lafforgue, Ngo, and Sakellaridis that implies the expected analytic properties of triple product L-functions. Time permitting, I will explain how to reduce this case of the Poisson summation conjecture to a simpler case in which spectral methods can be employed together with certain local compatibility statements. This is joint work with P. Gu, C-H. Hsu, and S. Leslie.
Alfio Fabio La Rosa (University of Luxembourg) Arithmetic applications of the trace formula and asymptotic orthogonality of tempered representations
In the first part of the talk, I will discuss an approach based on the trace formula to investigate the conjecture of K. Buzzard and T. Gee that every C-algebraic automorphic representation of a connected reductive algebraic group defined over a number field is C-arithmetic.
In the second part, I will present a joint work with Anne-Marie Aubert dedicated to the proof of the Archimedean case of the asymptotic form of Schur's orthogonality for K-finite matrix coefficients of tempered representations of semisimple groups proposed by D. Kazhdan and A. Yom Din.
Qing Liu (Université de Bordeaux) Resolution of singularities of double covers of regular surfaces
In this talk I will explain how to apply Lipman's method to resolve the singularities of double covers of regular surfaces. This leads in particular to an algorithm to finding a regular model over the ring of integers for hyperelliptic curves defined over the rational numbers. Such a regular model contains quite a few interesting information concerning the arithmetical properties of the curves.
Last modification: December 17, 2024.