Dynamics of the Weil-Petersson geodesic flow

June 18 to June 22, 2012

at the

American Institute of Mathematics, San Jose, California

organized by

Keith Burns, Howard Masur, Amie Wilkinson, and Scott Wolpert

Original Announcement

This workshop will be devoted to the study of recent advances in understanding deformations of Riemann surfaces via the Weil-Petersson metric on Teichmuller and moduli spaces. The works of Brock, Liu-Sun-Yau, McMullen, Mirzakhani, and Wolpert have opened new exploration on two fronts: establishing novel connections to topics in geometry, topology and dynamics; and understanding fine properties of the metric itself, such as comparison estimates and curvature expansions. Further advances have come from developing the relation of the metric to problems in 2 and 3-dimensional hyperbolic geometry and in understanding the dynamics of the Weil-Petersson geodesic flow.

This work has brought together a variety of ideas from disparate areas of mathematics. One of the main goals of this workshop will be to bring researchers from different cultures together to study problems of common interest. A secondary goal is to explore the possibility that ideas from classical Teichmuller theory might be relevant in the study of representations of surface groups into higher rank Lie groups, the so-called "higher Teichmuller theory". The major topics of the workshop will be:

  1. higher statistical properties of the Weil-Petersson flow such as rates of mixing, central limit theorem, and invariant measures;
  2. the relationship of the Weil-Petersson metric to hyperbolic 3-manifolds and ending laminations;
  3. possible connections of the Weil-Petersson and Teichmuller metrics to higher Teichmuller theory.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Holomorphic cubic differentials and minimal Lagrangian surfaces in CH2
by  Zheng Huang, John Loftin, and Marcello Lucia,  Math. Res. Lett. 20 (2013), no. 3, 501-520  MR3162843