调和分析和偏微分方程研讨班：Can you hear your location on a manifold?

中科院数学与系统科学研究院

数学研究所

调和分析及其应用研究中心

学术报告

调和分析和偏微分方程研讨班

报告人：席亚昆（浙江大学）

题  目：Can you hear your location on a manifold?

时  间：2023.05.23（星期二）16:30-17:30

地  点：数学院南楼N802

摘  要：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.