Hyperbolic surfaces with small eigenvalues.

by Mr Sugata Mondal (Institute Mathematique de Toulouse, France)

Friday 13 Sept 2013, 16:00 → 17:00 Asia/Kolkata

AG-77 (Colaba Campus)

We shall talk about eigenvalues of the Laplace operator on hyperbolic surfaces. The main focus of the talk would be on 'small eigenvalues' i.e. eigenvalues in the interval (0, 1/4]. We shall recall a method, due to P. Buser, to show that surfaces with small eigenvalues do exist. If time permits, we shall discuss the result of Otal-Rosas on upper bound on the number of such eigenvalues depending on the topology of the surface.