Everytopic Seminar

 September 26th, 2008, 1:40 pm – 3:00pm, Goldsmith 226

 

 

Title: Lattice surfaces, the Veech dichotomy and generalizations

Speaker: Barak Weiss (Ben Gurion University, Israel)

 

Abstract:

Translation surfaces are objects which arise naturally in

several different mathematical domains, e.g. complex analysis, topology of

surface homeomorphisms, and the study of rational polygonal billiards. The

symmetries of a given translation surface M naturally give rise to a

subgroup of SL(2,R) called the Veech group of M. For generic M the Veech

group is trivial, however in many cases it is quite large. In particular M

is called a lattice surface if its Veech group is a lattice in SL(2,R). In

1989 Veech constructed many examples of lattice surfaces and showed that

they have very interesting dynamical properties. We will present recent

joint work with John Smillie and Pascal Hubert extending some of Veech's

results. No prior acquaintance with Veech surfaces will be assumed, and

pictures will be shown.