PHN0eWxlPgouZnVzaW9uLWNvbnRlbnQtYm94ZXMgLmZ1c2lvbi1jb2x1bW4gewoJbWFyZ2luLWJvdHRvbTogMHB4Owp9Cjwvc3R5bGU+ The Faculty of Science and Technology of the University of Macau hosted a distinguished Talk by Prof. Fanghua Lin, a world-renowned mathematician and member of the U.S. National Academy of Sciences. In his lecture, Prof. Lin revisited the classical yet deeply challenging topic of extreme problems associated with Dirichlet eigenvalues of the Laplacian. The talk began with an introduction to Weyl’s asymptotic formula, which describes the qualitative behavior of large eigenvalues on bounded domains in Euclidean space. Prof. Lin skillfully bridged classical results with contemporary research, highlighting recent advances in obtaining more quantitative estimates. He discussed the well-known Polya’s conjecture and explored several natural variational and extreme problems related to eigenvalues, offering insight into both theoretical and applied implications. ...