Discrete lattice orbits in the plane

22.06.2020 14:20 - 15:05

Claire Burrin (Rutgers University)

Let a lattice in SL(2,R) act linearly on the plane, its orbits will be either dense or discrete. If we consider a discrete lattice orbit, how are its points distributed around the plane? This simple question has important bearings in several topical parts of dynamics, while being closely connected with the structure of the spectrum of the Laplacian. We will start with some special cases to illustrate the difficulties involved, and then move on to present the current state-of-the-art. Time permitting, I will then discuss some possible avenues for future progress. This is based on joint work with Amos Nevo, Rene Rühr, and Barak Weiss.

Fakultät für Mathematik
Zoom Meeting