## Counting integral points in certain homogeneous spaces

**报告题目**：Counting integral points in certain homogeneous spaces

**报告人**：徐飞教授 (首都师范大学数学系)

**时间**：2013年3月21日（星期四）16:00-17:00

**地点**：理科楼数学系A404报告厅

**摘要****:** The Hardy-Littlewood circle method is the classical method for counting integral points.Once this method can be applied, the asymptotic formula of the number of integral points will be given by the product of the number of local solutions and the local-global principle will be true.

However, the local-global principle can not be held in general. In this talk, I will explain the asymptotic formula of the number of integral points in non-compact symmetric homogeneous spaces of semi-simple simply connected algebraic groups is given by the average of the product of the number of local solutions twisted by the Brauer-Manin obstruction. As application, we will prove that the asymptotic formula of the number of integral matrices with a fixed irreducible characteristic polynomial over integers studied by Eskin-Mozes-Shah is equal to the product of the number of local integral solutions over all primes although the density function defined by Borovoi and Rudnick is not trivial in general. This is a joint work with Dasheng Wei.

**联系人：**姚家燕