# Flat Surfaces and Dynamics of Moduli Space (16w5010)

## Organizers

(University of Washington)

(Goethe Universität Frankfurt Am Main)

## Description

The Casa Matemática Oaxaca (CMO) will host the "Flat Surfaces and Dynamics of Moduli Space" workshop from May 8th to May 13th, 2016.

The long-term behavior of trajectories of a single ball on a polygonal billiard table
is a very interesting dynamical system. The first results date back to Fagnano in the
16th century and many central questions are still open.
If the angles of the table are rational multiples of $\pi$, an unfolding construction yields
a flat Riemann surface and the dynamics on the billiard table is closely tied with a renormalization dynamics
given by a Lie group action on the moduli space of these flat Riemann surfaces.
\par
The purpose of this workshop is to push further the fruitful concept of adapting
methods from dynamics on homogeneous spaces to dynamics on the moduli space of flat Riemann surfaces,
although this is not a homogeneous space. Recently, major progress has been made
on orbit closures, but the classification problem is far from solved and steps
in this direction will be discussed at the workshop. Deeper understanding of flat
surfaces, and in particular infinite area flat surfaces are making it possible to also tackle problems on billiard tables without
rationality conditions.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry.

The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.