Zu Chongzhi Center Colloquium

Date and Time (China standard time): Friday, September 15, 4:30-5:30 pm

Location: WDR 1007

Zoom: 917 8254 0311; Passcode: dkumath

Title: Can You Hear Where a Drum is Struck?

Speaker: Yakun Xi

Bio: Yakun Xi is a harmonic analyst at School of Mathematical Sciences, Zhejiang University. In 2017, he received his Ph.D. from Johns Hopkins University, advised by Prof. Christopher D. Sogge. He worked as a visiting assistant professor at University of Rochester from 2017 to 2020, and joined Zhejiang University in 2020.

Abstract:  When you hit a drum, the sound it makes is a mix of overtones with frequencies corresponding to the drum’s Laplace eigenvalues. A classic paper by Kac [“Can one hear the shape of a drum?” 1966] asks if the frequencies of these overtones uniquely determine the shape of the drum head. This question is still richly studied.

We recently posed a related question: Can one hear where a drum is struck? Imagine you know a drum’s shape. Could you determine where it is struck, up to symmetry, by listening also to the amplitudes of these overtones?

In this talk, I will state this problem precisely, give additional physical interpretations, work some examples, and share our results so far.