报告人简介：Ayman Kachmar obtained his Ph.d from the University of Paris-Sud in 2007, under the supervision of B. Helffer. Then he held a post-doctoral position in the University of Aarhus under the supervision of S. Fournais. Since 2014, he is a professor of mathematics in the Lebanese University. His research interests are in the mathematical analysis of the Ginzburg-Landau model of superconductivity, the Landau-deGennes model of liquid crystals and the spectral theory of the magnetic Laplace operator.
The spectrum of the Laplace operator in a bounded domain consists of a sequence of discrete eigenvalues. The celebrated min-max principle lists the eigenvalues in a variational manner counting multiplicities. In some cases, the eigenvalues are known to be simple. In joint works with N. Raymond and B. Helffer, we addressed this question in some asymptotic limits. In this talk, I will present the results valid in a thin domain, where the thickness of the domain is measured by a parameter that tends to 0. Assuming that the domain enjoys certain symmetry properties, the first two eigenvalues are simple and the spectral gap can be precisely estimated. Adding a magnetic flux, an oscillatory behavior in the leading order term is observed.
主持人： 潘兴斌 教授