报告人：魏巧玲（首都师范大学）

报告题目：On deformational spectral rigidity of convex symmetric planar domains

报告摘要：This talk is related to the famous question "Can you hear the shape of drum?" by M.Kac in 1960'. That is, whether a planar domain Ω can be uniquely determined by its Laplace spectrum consisting of eigenvalues of a Dirichlet problem . In general, there are counterexamples.Meanwhile, from dynamical aspect, there is length spectrum consisting of perimeters of all periodic orbits of a billiard problem inside Ω. The Laplace and length spectra are closely related, generically the first determines the second.During the talk we show that a planar axis symmetric domain close to the circle can not be smoothly deformed preserving the length spectrum unless the deformation is a rigid motion. This is a joint work with J. De Simoi and V.Kaloshin.

报告时间：2018年7月6日（星期五）下午14：30--15：30

报告地点：科技楼（南）702室