Speaker：YU Jun（ BICMR）
Place：Room 1218, School of Mathematical Sciences
Detail：A famous question in differential geometry asked by Marc Kac: "Can one hear the shape of a drum?" It concerns the comparison of Laplace spectra on different Riemannian manifolds. By studying particular kind of manifolds like flat tori and local symmetric spaces, and with Sunada's method and torus action method, there are plenty of examples of isospectral manifolds with the same or different local geometry. I will give a brief account of some history of this subject and the first examples of isospectral manifolds which are simply connected but not homotopic, due to Jinpeng An, Jiu-Kang Yu and the speaker.