香蕉视频

Title:聽Applications of algebra and topology to isoperimetric eigenvalue inequalities

Abstract:聽Spectrum of the Laplace-Beltrami operator is one of the fundamental invariants of a Riemannian manifold. Finding the optimal isoperimetric inequalities for its eigenvalues is a classical problem of spectral geometry going back to J. Hersch, P. Li and S.-T. Yau. One of the main attractions of this problem is the variety of methods employed to study it. In the present talk we demonstrate this feature and, in particular, outline the connections to the theory of minimal surfaces, algebraic geometry and topology. These include recent applications of moduli spaces and cobordism theory. The talk is based on joint works with V. Medvedev, N. Nadirashvili, A. Penskoi and I. Polterovich.