I will describe joint work with John Smillie giving finiteness

results for sets of lattice surfaces. A lattice surface is a pair $(S,q)$,

where $S$ is a compact orientable surface and $q$ is a translation structure

(or complex structure with a holomorphic 1-form) whose stabilizer in

$SL(2,{\bf R})$ is a lattice. Veech showed that non-arithmetic lattices may arise

and that billiards connected with lattice surfaces have nice dynamical

propertries (“Veech dichotomy”). We give concrete conditions for lattice

surfaces, and characterize them dynamically in terms of both the

corresponding billiard and the $SL(2,{\bf R})$ action. We also show that there is

a finite number of lattice surfaces with a fixed lower bound on the area

of any triangle, and that fixing the genus of $S$, there is only a finite

number with a fixed upper bound on the covolume.

# Isolation theorems for quadratic differentials

Event time:

Tuesday, January 18, 2005 - 11:00am to Monday, January 17, 2005 - 7:00pm

Location:

431 DL

Speaker:

Barak Weiss

Speaker affiliation:

Ben Gurion University

Event description: