Non-accumulation of periodic torus orbits

Informal Group Action Seminar
Topic:Non-accumulation of periodic torus orbits
Speaker:Ilya Khayutin
Affiliation:Princeton University; Veblen Research Instructor, School of Mathematics
Date:Wednesday, December 12
Time/Room:2:00pm - 3:15pm/Simonyi Hall 101

The "linearization" technique is a powerful method in homogeneous dynamics to control the time a unipotent orbit spends in the vicinity of a closed homogeneous subset. This method relies on the polynomial nature of a unipotent flow and does not extend to diagonalizable actions. 

I will describe a new arithmetic approach to bound the accumulation of periodic orbits of higher-rank diagonalizable groups. This method plays a major role in the recent progress on the Michel-Venkatesh mixing conjecture.