Title: Renormalization in translation surfaces with symmetry
Speaker: Pat Hooper
Speaker Info: Northwestern University
I will explain a simple case of renormalization. I will begin by discussing a construction of Thurston which produces especially symmetric surfaces by gluing together rectangles in the plane by translations. In particular, a non-trivial subgroup G of SL(2, R) acts on these surfaces.Date: Thursday, December 3, 2009
One can consider flows in various directions on these surfaces. In directions compatible with G, we can use the G action to renormalize the flow. Using this idea we can prove that the flow in such a direction is uniquely ergodic.
Unique ergodicity is in fact a consequence of a theorem of Masur. However, I hope to give a more accessible talk by restricting attention to this specific case. Furthermore, arguments in this talk generalize to infinite genus surfaces. I will not discuss these generalizations in detail.