Ratner Theory and Strata?

John Smillie
Cornell University

Questions about polygonal billiards lead to the study of moduli spaces of translation surfaces or "strata". There are intriguing parallels between strata and homogeneous spaces and there has been a fruitful migration of ideas from homogeneous dynamics to "Teichmuller dynamics" on strata. One pivotal question is the extent to which Ratner theory applies to strata. I will discuss positive results of Eskin and Mirzakhani and describe negative results obtained with Barak Weiss.

Back to Workshop II: Dynamics of Groups and Rational Maps