Abstract

A period integral is the average of a Laplace eigenfunction over a compact submanifold. Much like for the Weyl law, one can obtain improved estimates on period integrals given geometric or dynamical assumptions on the geodesic flow. While there are many results improving bounds on period integrals, there have been none which improve the remainder of the corresponding sum formula. In this talk, we discuss a recent joint work with Emmett Wyman. We show that an improvement to the remainder term of this sum formula reveals a lower-order oscillating term whose behavior can be described by the dynamics of the geodesic flow. Moreover, this oscillating second term illuminates bounds on period integrals.

Speaker

席亚昆，理学博士，浙江大学数学科学学院研究员，博士生导师。2008-2012本科就读于浙江大学数学系，获数学与应用数学学士学位。2012-2017于美国约翰霍普金斯大学攻读博士学位，师从国际著名调和分析专家Christopher D. Sogge教授。2017-2020在美国罗切斯特大学任客座助理教授，2020年八月加入浙江大学数学科学学院任研究员。其研究领域主要为经典调和分析以及流形上的调和分析问题，文章发表于Camb J Math, Amer J Math, Comm Math Phys, Trans AMS, J Func Anal等国际著名数学期刊。