Date:	Tue, February 18, 2014
Time:	14:15
Place:	Research I Seminar Room

Abstract: An average sum on GL2(Z)-orbits of square-tiled surfaces. Abstract: A square-tiled surface is a covering of the standard torus ramified above at most one point. Such a surface is endowed with a flat metric having conical singularities. If the flat metric has only one conical singularity, with angle 6π, then the surface is said to belong to the stratum H(2). There is a natural action of the group GL2(Z) on square-tiled surfaces which preserves the stratum.

I consider a simple rational-valued function on square-tiled surfaces in H(2), and show that the average of this function on any primitive GL2(Z)-orbit is exactly 1/3 (which is also the non-trivial Lyapunov exponent of the Kontsevich-Zorich cocycle).