Abstract:
An interesting example of a dynamical system is given by
billiards in a polygon in the plane. An important special case is if the
vertex angles are rational multiples of pi. A standard unfolding process
leads to a flow on what is called a translation surface. A classical case
is the linear flow on a flat torus. It turns out that one often gets
information about the flow on the individual surface by studying a
different dynamical system; namely the action of the group SL(2,R) on
families or moduli spaces of surfaces. If the stabilizer of a point by
this action is a lattice in SL(2,R) then the surface is called a Veech
surface. If the surface is a Veech surface, then the flows on that
surface have nice dynamics. We will discuss this whole setup and
developments in the subject over the last several years.
