Diophantine approximation problems for groups of toral automorphisms.
Ergodic Theory and Dynamical Systems Seminar
23rd November 2017, 3:00 pm – 4:00 pm
Howard House, 4th Floor Seminar Room
I will present sharp rates for a shrinking target problem for the action of arbitrary subgroups of SL(2,Z) on the 2-torus. This can also be viewed as a noncommutative Diophantine approximation problem. The methods require construction of spectrally optimal random walks on groups acting properly cocompactly on Gromov hyperbolic spaces. Additionally, I will explain how similar estimates for this problem in higher dimension can be obtained using harmonic analysis.