Juan Souto

Abstract: We prove that every closed, smooth manifold of at least dimension 3 admits a sequence of Riemannian metrics with pinched curvature, volume tending to infinity but whose first eigenvalue of the Laplacian remains bounded away from 0. As a...

Abstract Studying Gromov-Hausdorff limits of sequences of Riemannian manifolds $(M_i)$ satisfying suitable conditions on their local geometry is an extremely fruitful idea. However, in the most interesting case that the diameter of $M_i$ grows...

Consider the moduli space M_{g,s} of Riemann surfaces of genus g with s marked points as an orbifold. In this talk I will determine all (non-constant) holomorphic maps M_{g,s}\to M_{g',s'} if g\ge 6 and g'\le 2g-2. This is joint work with Javier...