SSE Weekly Colloquium | 理工学院系列研讨会第三讲邀请
Can One Hear the Shape of a Drum?
The title of this talk was a question praised by Lipman Bers and then made famous by Marc Kac's 1966 expository article. The problem here is to determine whether two domains are congruent if they have the same vibration frequencies (i.e., the spectrum of the Laplacian). It turns out that the answer is negative for general plane domains. However, one can still obtain information about a geometric shape from its frequencies. This problem raises the research area of spectral geometry that is closely related to the index theory, and it yields fruitful results in analysis, geometry, topology, and probability. In this talk, we shall describe, though very briefly, the attempts and results around this topic. We shall outline the contributions of Euler, Gauss, Bonnet, Chern, Weyl, Atiyah, Singer, Patodi, among many others. If time allows, we will also discuss the recent progress of non-elliptic operators on contact structures along the same lines.
Prof. LI Yutian received his B.Sc. degree in Mathematics and Applied Mathematics from Jilin University in 2005, and the MPhil and PhD degrees in Mathematics both from City University of Hong Kong in 2007 and 2010 respectively. He was a Postdoc Research Fellow at Liu Bie Ju Centre for Mathematical Sciences of City University of Hong Kong from 2010 to 2012. He then worked at Hong Kong Baptist University as a Research Assistant Professor from 2012 to 2017. He Joined the School of Science and Engineering of The Chinese University of Hong Kong, Shenzhen as an Assistant Professor in December 2017.
Prof. Li’s research interests include: Partial differential equations, Applied analysis, Scientific computing, Mathematical finances. He has published more than 20 papers in recognized journals in mathematics, applied mathematics, engineering and finance, including:
Studies in Applied Mathematics, Applied Mathematical Letters, Analysis and Applications, Constructive Approximations, Proceedings of the Royal Society London A, Discrete and Continuous Dynamical Systems, Journal of Scientific Computing, Optics Expresses, IEEE Transaction on Microwave Theory and Technologies, Quantitative Finance, etc.