# Complex Analysis and Dynamics Seminar

## Department of MathematicsGraduate Center of CUNY

### Fall 2014:

#### Sep 5: Max Fortier Bourque (Graduate Center of CUNY)Moving one Riemann Surface Inside Another

In this talk, I will sketch a proof of the following parametric homotopy principle: If two holomorphic embeddings between Riemann surfaces are homotopic, then they are isotopic through holomorphic embeddings. The proof uses a generalization of Teichmuller's theorem for quasiconformal embeddings, the geometry of quadratic differentials, and Gardiner's variational formula for extremal length.

#### Sep 12: Feng Luo (Rutgers University)A Dilogarithm Identity on the Moduli Space of Curves

We establish an identity for closed hyperbolic surfaces whose terms depend on the dilogarithms of the lengths of simple closed geodesics in all 3-holed spheres and 1-holed tori in the surface. This is joint work with Ser Peow Tan.

#### Sep 19: Yunhui Wu (Rice University) Translation Lengths of Parabolic Isometries of CAT(0) Spaces and its Application to the Geometry and Topology of Hadamard Manifolds

A CAT(0) space is a complete path-metric space with a certain inequality property. In this talk, we will discuss the translation length of parabolic isometries of CAT(0) spaces. As an application, we will connect several open problems and conjectures on Hadamard manifolds and moduli spaces of closed surfaces.