报告学者: 任金波

报告人所在单位: 厦门大学数学科学学院

报告人职称/职务及学术头衔:教授

报告时间: 2024年12月30日(周一) 14:00-16:00

报告地点：逸夫309

报告内容: An abstract group is said to have the  {\it 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 $K$ {\it never} has (BG).

Moreover, I will introduce our newly obtained asymptotic formula for counting the elements of a ``purely exponential parametrization'' (PEP) set inside $GL_n(K)$ ($K$ is a number field) when ordered by heights, together with some applications of this formula.

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.

 

 

报告人简介: 任金波,厦门大学数学科学学院教授。任老师博士毕业于法国巴黎十一大学，曾在美国弗吉尼亚大学和普林斯顿高等研究所做博士后。他的研究集中于丢番图问题和算术群的性质，其工作发表在Invent. Math., Compositio Math.等知名期刊上。