*时间：2022年06月29日 09:00-10:00

*地点：腾讯会议：684-128-729 会议密码：220629

*主讲人：任金波

*主持人：陈苗芬 副教授

*讲座内容简介：

 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 semisimple rigidity, Kazhdan's property (T) and Serre's congruence subgroup problem.

In this talk, I will explain how to use the Schlickewei-Schmidt subspace theorem in Diophantine approximation to prove that the distribution of the points of a set of matrices over a number field $F$ with (BG) by certain fixed semi-simple (diagonalizable) elements is of at most logarithmic size when ordered by height. Moreover, one obtains that a linear group $\Gamma \subset \mathrm{GL}_n(K)$ over a field $K$ of characteristic zero admits a {\it purely exponential parametrization} if and only if it is finitely generated and the connected component of its Zariski closure is a torus.

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

*主讲人简介：

任金波，现任美国IAS学者。曾任弗吉尼亚大学博士后，博士毕业于法国巴黎萨克雷大学，师从Emmanuel ULLMO教授。他的研究领域为数论。