基础数学系学术报告

An estimate for spherical functions on SL(3,R)

李晓承

（南京理工大学）

报告时间：10：30-11：30，2025-11-25（星期二）

报告地点：沙河校区主楼E806

内容简介：We prove an estimate for spherical functions $\varphi_\lambda(a)$ on SL(3,R), establishing uniform decay in the spectral parameter $\lambda$ when the group variable $a$ is restricted to a compact subset of the abelian subgroup $A$. In the case of SL(3,R), it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when $\lambda$ and $a$ vary.

报告人简介：李晓承，现任职于南京理工大学数学与统计学院。本科毕业于中国科学技术大学，博士毕业于美国威斯康星大学麦迪逊分校；先后在北京大学北京国际数学研究中心、山东大学数据科学研究院从事博士后研究，主要研究方向为调和分析和自守形式。

邀请人：吕恒飞  

欢迎大家参加！