Bilu's equidistribution theorem for non-Galois invariant sets

Organizers

Hansheng Diao, Heng Du, Yueke Hu,

Bin Xu, Yihang Zhu, Huajie Li

Speaker

Arnaud Plessis (BIMSA)

Time

Monday, 10:00- 11:00 am

December 15, 2025

Venue

B627

Shuangqing Complex Building A

Abstract

Denote by h the (absolute, logarithmic) Weil height. The celebrated Bilu's equidistribution theorem claims that for any sequence (x_n)_n of algebraic numbers satisfying [Q(x_n):Q] —> +\infty and h(x_n) --> 0, the sequence of Galois orbits of x_n is equidistributed around the unit circle.

Following a method due to Mignotte, I will explain why every sequence (S_n)_n of finite subsets of algebraic numbers satisfying # S_n —> +\infty and \sum_{\alpha \in S_n} (h(\alpha)/ # S_n) —> 0 is equidistributed "in average" around the unit circle. This is joint work with Amoroso.

About the Speaker

Arnaud Plessis is an assistant professor at BIMSA from September 2023. His research is mainly focused on diophantine geometry. He obtained his Phd. thesis in 2019 at Université de Caen Normandie. Before joining BIMSA, he has been Attaché Temporaire d'Enseignement et de Recherche (a kind of postdoctoral with course duties) at Université Grenoble Alpes from September 2019 to August 2020. Then, he has been postdoctor at Morningside Center of Mathematics, Chinese Academy of Sciences, from September 2020 to August 2023.