|Date: Monday, April 04, 2022
Location: 3096 East Hall (4:00 PM to 5:00 PM)
Title: Counting pairs of saddle connections on translation surfaces
Abstract: A translation surface can be thought of as a polygon in the plane with pairs of sides identified by parallel translation. A saddle connection is a straight line joining the vertices of the polygon. It determines a vector in the plane. The problem of the asymptotics of the number of saddles less than a given length was initiated by W.Veech. I will recall some of the known results in this subject. I will then discuss the problem of counting pairs of saddle connections. The motivation is in part a result of J. Smillie and B. Weiss who showed that for a Veech or lattice surface there are no small (virtual) area triangles so any pair of saddle connections with small cross product are parallel. I will discuss for a generic surface the asymptotics of the number of pairs of saddle connections which have a bound on their cross product. This is joint work with Jayadev Athreya and Samantha Fairchild.
Speaker: Howard Masur
Institution: University of Chicago
Event Organizer: Alex Wright