|Contemporary Topics in Teichmuller Theory by Riemannian Geometric Techniques|
|Instructor：||Michael Wolf [Rice University]|
|Place：||Conference Room 1， Floor 1, Jin Chun Yuan West Building|
We introduce Teichmuller space, an analytically tractable cover of Riemann’s moduli space of curves. We develop a coherent method of studying this space through Riemannian geometric methods. We hope to cover the basic definitions, the Weil-Petersson metric and curvature tensor (Royden, Tromba, Wolpert), the convexity of the length function (Wolpert), and the equivalence of the Thurston metric with the Weil-Petersson metric from a single perspective. If time allows, we may venture into the space of complex projective and convex real projective structures on a surface.
Some familiarity with complex analysis; the rudiments of Riemannian geometry including Riemannian metrics, curvature tensors and first & second variation formulas; the definition and some elementary properties of Riemann surfaces, including the rudiments of hyperbolic geometry.
Jost, J. Compact Riemann surfaces
Jost, J. Two-Dimensional Geometric Variational Problems
The Weil-Petersson Hessian of Length on Teichmuller Space, J. Differential Geom. 91(2012), 129-169