报告题目：Bounded Generation: a diophantine approximation approach

报告时间：2025-09-19  14:30-15:30

报 告 人：任金波 教授（厦门大学）

报告地点：雷军科技楼五楼报告厅（520）

Abstract：An abstract group is said to have the bounded generation property (BG) if it can be written as a product of finitely many cyclic subgroups. Being a purely combinatorial notion, bounded generation has close relation with many group theoretical problems including semi-simple rigidity, Kazhdan's property (T) and Serre's Congruence Subgroup Problem.

This talk is devoted to explaining how to use the Laurent's theorem in Diophantine approximation to prove that an infinite S-arithmetic subgroup of an anisotropic linear algebraic group G over a number field K never has (BG).

Moreover, I will introduce our newly obtained asymptotic formula for counting the elements of a ''purely exponential parametrization'' (PEP) set inside GLn (K) (K is a number field) when ordered by heights, together with its crucial applications to (BG).

The novelty of this project relies on the deep subspace theorem by Schlickewei-Schmidt as well as the theory of generic elements by Prasad-Rapinchuk.

This is joint work with Corvaja, Demeio, Rapinchuk and Zannier.