Thick surfaces and the diameter of moduli space

Jeudi 13 juin 14:00-15:00 - Jing Tao - University of Oklahoma

Résumé : Let M_g be the moduli space of hyperbolic surfaces of genus g. The thick part of M_g is set the surfaces with a lower bound on the length of the shortest curve. The thick part is compact, and hence has finite diameter with respect to any metric endowed on M_g. In joint work with Kasra Rafi, we showed that, with respect to the Teichmuller or Thurston metric, the diameter of the thick part has order log(g). In this talk, I will explain how to construct pairs of surfaces that realize this diameter. There are essentially two reasons for surfaces to be far way from each other : combinatorial and geometric. I will explain what these two notions are and construct four interesting examples of hyperbolic surfaces. Three of these examples will be constructed using trivalent graphs, and the fourth will be a variation of Buser’s hairy torus.

Lieu : IMO, salle 2L8

Notes de dernières minutes : L’exposé sera précédé d’un café culturel assuré à 13h par Camille Horbez.

Thick surfaces and the diameter of moduli space  Version PDF