Gaps of saddle connection directions for some branched covers of tori
Anthony Sanchez (U. Washington Math)
Abstract: Consider the class of translation surfaces given by gluing two identical tori along a slit. Every such surface has genus two and two cone-type singularities of angle $4\pi$. There is a distinguished set of geodesics called saddle connections that are the geodesics between cone points. We can recover a vector in the plane representing the saddle connection by keeping track of the amount that the saddle connection moves in the vertical and horizontal direction. How random is the set of saddle connections? We shed light to this question by considering the gap distribution of slopes of saddle connections. Zoom Meeting ID: 460 321 230. Email clein for password.