|Location:||MSRI: Simons Auditorium|
This is a joint work with Bainbridge and Smillie, in which we import ideas from homogeneous flows, and specifically Ratner's measure classification and the Dani-Margulis linearization method, to the study of dynamics on strata of translation surfaces in a restricted setting. We discuss dynamics of the horocycle flow on the eigenform loci discovered by Calta and McMullen. We reprove and improve the measure classification result of Calta and Wortman, and obtain a corresponding orbit-closure classification. We show that every orbit is equidistributed in its orbit-closure. We also obtain some statements regarding limits of sequences of measures arising in some counting problems.
I will state and motivate the results and give a sample of the challenges presented by the translation surface setting. I will try to make it understandable to members of both MSRI programs.