Speaker：Lihan Wang (California State University – Long Beach)

Time：2023-6-15, 10:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

In 1966, Mark Kac asked the famous question “Can one hear the shape of a Drum ?”. In his article with this question as the title, he translates this question to eigenvalue problems of a domain in R^2. That is, can you tell the shape of a domain if eigenvalues are known. This question can be generalized from Euclidean spaces to curved spaces, especially non-compact manifolds. In this talk, we will recall the history of this classic question first. Then we will explain the generalized question in manifolds and known results. In the last, we will discuss our recent results for non-compact Kahler manifolds in this direction.