学术报告（韦国芳 2026.7.8）

摘要：The fundamental (or mass) gap refers to the difference between the first two eigenvalues of the Laplacian or more generally for Schr\"{o}dinger operators. It is a very interesting quantity both in mathematics and physics as the eigenvalues are possible allowed energy values in quantum physics. We will survey many recent fantastic results for convex domains in Euclidean spaces, spheres, hyperbolic spaces and surfaces with positive curvature with Dirichlet boundary conditions, starting with the breakthrough of Andrews-Clutterbuck.  Then we will present a recent work on horoconvex domains in the hyperbolic space. This include a result joint with Ling Xiao and very recent one using AI.