Sai-Kee Yeung, Purdue U., USA

Geometric results in Teichmüller and moduli space of curves

We would like to discuss a few results on Teichmuller and moduli spaces of curves that are obtained using methods of complex geometry. These include a problem of Yau about quasi-isometry of invariant metrics, a question of Gromov about Kaehler hyperbolicity of the Bergman metric, and an analogue of Zucker's conjecture on the relation between L² cohomology and singular cohomology. Some geometric consequences would also be discussed.