2016
Nov
01

# Dynamics & probability: Asaf Katz (HUJI): Mixing and sparse ergodic theorems

2:00pm to 3:00pm

## Location:

Manchester building, Hebrew University of Jerusalem, (Room 209)

We consider Bourgain's sparse ergodic theorem for systems where quantitative mixing estimates are present. Focusing on the case of the horocyclic flow, we show how to use such

estimates in order to bound the dimension of the exceptional set, providing evidence towards conjectures by N. Shah, G. Margulis and P. Sarnak. Moreover we show that there exists a bound which is independent from the spectral gap. The proof uses techniques from homogeneous dynamics, automorphic representations and number theory.

estimates in order to bound the dimension of the exceptional set, providing evidence towards conjectures by N. Shah, G. Margulis and P. Sarnak. Moreover we show that there exists a bound which is independent from the spectral gap. The proof uses techniques from homogeneous dynamics, automorphic representations and number theory.