Speaker: Yakun XI (Zhejiang University)

Time： April 27, 16:00-17:00

Place： 5205

Title： Can you hear your location on a manifold?

Abstract： We introduce a variation on Kac's question, Can one hear the shape of a drum? Instead of trying to identify a compact manifold and its metric via its Laplace--Beltrami spectrum, we ask if it is possible to uniquely identify a point x on the manifold, up to symmetry, from its pointwise Weyl counting function. This problem has a physical interpretation. You are placed at an arbitrary location in a familiar room with your eyes closed. Can you identify your location in the room by clapping your hands once and listening to the resulting echos and reverberations? Our main result provides an affirmative answer to this question for a generic class of metrics.