Joint meeting, April 13-14 2026, Bordeaux
Speakers:
Gaurav Aggarwal (University of Zürich)
Pascal Autissier (Bordeaux)
Alexandre Bailleul (Paris Saclay)
Filippo Berta (EPFL)
Régis de la Bretèche (Université Paris Cité)
Alexandre de Faveri (EPFL)
April 13
- 10:30-11:00: Coffee and pastries
- 11:00-12:30: Gaurav Aggarwal The Doeblin–Lenstra conjecture: effective results and central limit theorems
- 12:30-14:00: Buffet lunch
- 14:00-15:00: Alexandre Bailleul An effective Kronecker-Weyl equidistribution theorem and an application to generalized Skewes' numbers
- 15:00-15:30: Coffee and pastries
- 15:30-16:30: Pascal Autissier Iterated polynomials are dense
- 19h: Conference dinner
The Doeblin–Lenstra law is a classical result describing the limiting distribution of approximation errors arising from the continued fraction convergents of a typical real number. Originally conjectured by Doeblin and later rediscovered by Lenstra, the law was proved by Bosma, Jager, and Wiedijk (1983) using the ergodicity of the Gauss map. However, while the existence of this limit has long been known, the rate of convergence remained unknown. In this talk, we present the first effective convergence rates for the Doeblin–Lenstra law. We also establish analogous effective results for points sampled from self-similar fractal measures, such as the middle-third Cantor measure. Finally, we discuss extensions to higher dimensions and prove central limit theorems for the associated Diophantine statistics in each of these settings. This talk is based on joint work with Anish Ghosh.
Following the works of Rubinstein-Sarnak, the Kronecker-Weyl equidistribution theorem has become an important tool to study prime number races-type problems. In this joint work with M. Hayani and T. Untrau, we formulate an effective version of this equidistribution theorem in terms of 1-Wasserstein distance, that allows us to measure (conditionally on some effective linear independence assumption) how fast the underlying convergence of measure holds. As a byproduct, we obtain bounds on generalized Skewes' numbers, which are the locations of the first sign change in a prime number race.
Let K be an infinite field and r be a positive integer. In a joint work with Furter and Yasinsky, we show constructively that the map sending each polynomial P in K[X] to its r-th iterate has dense image, in various inductive limit topologies on the space K[X].
- 10:30-11:00: Coffee and pastries
- 11:00-12:00: Filippo Berta Subconvexity Problem on GL_3 over number fields: the twist aspect
- 14:00-15:00: Régis de la Bretèche Some results on the Erdös-Hooley Delta-function
- 15:00-15:30: Coffee and pastries
- 15:30-16:30: Alexandre de Faveri Mass equidistribution for lifts on hyperbolic 4-manifolds
In 2015 Munshi proved a subconvexity bound for L(\pi \times \chi, 1/2), where \pi is a fixed SL_3(Z) automorphic form and \chi ranges over primitive Dirichlet characters of (prime) conductor q going to infinity. In 2018, Holowinsky and Nelson discovered a shortcut -"degeneration to frequency zero" - that made the method much simpler. In this talk, I will explain how to implement Holowinsky and Nelson’s method for any number field using Jacquet--Piateski-Shapiro--Shalika integral representations of GL_3 x GL_1 L-functions. This allows us to prove, for every number field, a result analogous to that of Munshi and Holowinsky--Nelson.
We will present some recent results on the Erdöos-Hooley Delta-function : mean value, moments and normal order... This is about joint works with Gérald Tenenbaum.
I will discuss recent work with Zvi Shem-Tov proving QUE for the sequence of Pitale lifts, which are Hecke-Maass forms in hyperbolic 4-space constructed from half-integral weight forms (i.e. non-holomorphic analogues of the Saito-Kurokawa lifts). Our main innovation is the delicate construction of an amplifier with favorable geometric properties. This is the first successful use of the amplification method for escaping a non-tempered subgroup.