About:

This public talk was part of the "Shape Optimisation and Geometric Spectral Theory" workshop at ICMS.

We were delighted to welcome speaker Carolyn S. Gordon (she/her) to give this talk. As the speaker presented remotely, the in-person element of this event was a 'watch party' of the talk and a drinks reception.

Imagine that you have perfect hearing, enabling you to recognize even the most subtle change in frequencies. You hear but don't see first one possibly exotic-shaped (i.e., not necessarily round) drum being played and then another. Would you be able to tell whether the drums are identical or different? In the words of mathematician Mark Kac: "Can you hear the shape of a drum?"
This talk focused on Kac's question. We explored some affirmative answers, e.g., you can hear whether a drum is round. We also looked at some negative answers: constructions of different exotic-shaped membranes that produce the same sounds. Much more remains to be discovered!
Kac’s question is a fun example of the general problem of spectroscopy in which one attempts to gain information about an object from so-called "spectral data", e.g., determining the chemical composition of a celestial object from the spectrum of emitted light.