Event Type:

Department Colloquium

Date/Time:

Tuesday, April 15, 2008 - 09:00

Location:

*In Eugene* Willamette 100 (UO)

Local Speaker:

Abstract:

To study the dynamics of a point with ideal motion in a Euclidean triangle (reflecting off of the sides in a standard fashion) one can glue together copies of this "billiard table" into a flat surface. The standard matrix action on the plane induces a group of self-maps of this surface; Veech showed that when this group is a "lattice" the flat surface has "optimal" dynamics, similar to a flat torus.

Answering a question of Veech, jointly with P. Hubert we showed that the group can in general be infinitely generated. McMullen followed with further examples. We indicate some of the geometry --- flat, hyperbolic and algebraic --- of the various constructions.