[Binghamton Geometry Topology Seminar] This week: Ben Dozier

[jwilliams at math.binghamton.edu]

Thursday, Feb 21, 2:50pm in WH 100E.

Speaker: Ben Dozier (Stony Brook)

Title: Equidistribution of billiard trajectories and translation surfaces

Abstract: Consider a billiard ball bouncing around on a polygonal table. 
This dynamical system is surprisingly complex.  When the angles of the
table are rational, the billiard table can be "unfolded" to get a closed
surface with a natural flat geometry.  This is an example of a translation
surface.  Billiard trajectories on the original table unfold to straight
lines on the translation surface.  Translation surfaces form a moduli
space (which is a bundle over $M_g$, the moduli space of genus g Riemann
surfaces), and this space comes equipped with a natural action by
$SL_2(\mathbb R)$.  Through a technique of "renormalization", questions
about the dynamics on a fixed surface can be translated into questions
about the dynamics associated with this $SL_2(\mathbb R)$ action. The
$SL_2(\mathbb R)$ action is very rich, and analogies with homogeneous
dynamics can be leveraged.

Jenya is this week's host; please feel free to contact her about lunch
with the speaker.