[Distinguished Lecture] Variational Problems and Conjectures Concerning the Laplacian Eigenvalues
Time: 2023-05-22
Published By: Wenqiong Li
Speaker(s): Fanghua Lin (Courant Institute of Mathematical Sciences, New York University)
Time: 16:00-17:00 May 30, 2023
Venue: Lecture Hall, Jiayibing Building, Jingchunyuan 82, BICMR
Abstract: Eigenvalue Problems for the Laplacians are among the most-studied ones in classical analysis, partial differential equations, calculus of variations and mathematical physics. In this lecture I shall discuss some recent progress on a couple of extremum problems involving the Dirichlet eigenvalues of the Laplacian, including the well-known Polya's Conjecture. These problems have origins in shape optimization, pattern formation, ..., and even data science. Solutions of these problems may also be related to the theory of harmonic maps into singular spaces and free boundary problems involving vector-valued functions.
Bio-Sketch: Prof. Fanghua Lin is a Silver Professor of Mathematics at the Courant Institute of Mathematical Sciences, NYU. He holds a B.S. from Zhejiang University and a Ph.D. from the University of Minnesota. Prof. Lin is a world-leading expert in classical and applied analysis, partial differential equations, geometric measure theory, and calculus of variations. He has made outstanding contributions to harmonic maps, mathematical theory of liquid crystals, Ginzburg-Landau theory, homogenization, equations of classic and complex fluids, etc. He was elected as a Fellow of the American Academy of Arts and Sciences in 2004, Fellow of the AMS in 2014, and SIAM Fellow in 2022. He was awarded the Alfred P. Sloan Research Fellowship in 1989, Presidential Young Investigator for 1989-1994, the Outstanding Young Researcher Award from NSF-China in 1998, the Changjiang Chair Professorship in 1999, the M. Bocher Prize of American Mathematical Society in 2002, and the S.S. Chern Prize at ICCM in 2004. He was an invited speaker of ICM Kyoto in 1990.
