The Dynamics Lunch seminar meets regularly on Tuesdays at 12:00 at the lobby of the Manchester building. Speakers talk not about their own work, but rather about some interesting paper they read (can be classical or new), that they think might be interesting to a broad dynamical audience (many times it is attended also by people from combinatorics/analysis/group theory). Meanwhile all attendants eat fruit and sandwiches.

2018
Jun
26

# Dynamics Lunch: Jasmin Matz (Huji) ״Distribution of periodic orbits of the horocycle flow״

12:00pm to 1:00pm

## Location:

Manchester lounge

An old result of Hedlund tells us that there are no closed orbits for the horocycle flow on a compact Riemann surface M. The situation is different if M is non-compact in which case there is a one-parameter family of periodic orbits for every cusp of M. I want to talk about a result by Sarnak concerning the distribution of the such orbits in each of these families when their length goes to infinity. It turns out that these orbits become equidistributed in M and the rate of convergence can in fact be quantified in terms of spectral properties of the Eisenstein series on M.