報告題目：Inverse spectral problem for ellipses
報 告 人：Hamid Hezari 教授
所在單位：University of California, Irvine（加州大學爾灣分校）
報告時間：2024年3月28日 10:00
報告地點：ZOOM ID：203 271 7634， 密碼：123456
校内聯系人： 張凱 zhangkaimath@jlu.edu.cn
報告摘要：This talk is about Kac's inverse problem from 1966: "Can one hear the shape of a drum?" The question asks whether the frequencies of vibration of a bounded domain determine the shape of the domain. First we present a quick survey on the known results. Then we discuss the key connection between eigenvalues of the Laplacian and the dynamics of the billiard, which is governed by the so called “Poisson Summation Formula“. Finally we discuss our main theorem that "one can hear the shape of nearly circular ellipses". This was a joint work with Steve Zelditch (9/13/1953 – 9/11/2022).
報告人簡介： Prof. Hezari obtained his PhD from Johns Hopkins University in 2009. Following that, he served as a CLE Moore instructor at MIT from 2009 to 2012. During the fall of 2010, he held a postdoctoral position at the MSRI program on inverse problems. Currently, he holds a professorial position at UCI.
His research primarily focuses on analysis and PDEs. Prof. Hezari has a keen interest in semiclassical/microlocal analysis and its diverse applications in PDE and mathematical physics, particularly in spectral geometry and quantum chaos. Notably, he has contributed significantly to the field with 28 high-quality publications, including works published in Annals.
