Event № 563
It is known that for most translation surfaces the number of saddle connections whose length is less than T grows asymptotically like T^2 by works of Eskin and Masur.One main idea in their proof is to use ergodicity of the SL(2,R) action on the space of translation surfaces. We will review the dynamically part of their proof. It is nowknown that this action also exhibits a spectral gap which allows one to conclude an additional error term. This effectivization is joint work with Amos Nevo and Barak Weiss.