Learning Seminar on Dynamical Systems and Ergodic Theory and Related Topics
Fall Semester of 2022
Organized by Yunping Jiang and Enrique Pujals
Friday, 11:00 pm – 1:00 pm Room 3212
September 16, Organization Meeting
September 23, Tao Chen, non-ergodicity of some transcendental meromorphic functions
September 30, Conversation with Professor Enrique Pujals (all students are welcome)
October 7, Enrique Pujals, Axiomatizing unimodality for surface diffeomorphisms
October 14, Yunping Jiang, Geometry in Furstenberg conjecture
October 21, Yunshan Jiang, Unitary representations of simple Lie groups
Abstract: Let a "special" Lie group G (like SL(2,R)) acts on a probability space X in a good way: preserves the measure
and G will have a unitary representation on the L^2 functions space. Then we can say a lot about the ergodicity
and mixing properties about this action, like "the ergodicity implies the action will also be mixing".
This is called the Howe-Moore theorem and it has a lot of applications. For example, the geodesic flow
and horocycle flow on the unit tangent bundle of a hyperbolic surface with finite area are ergodic and mixing.
Also by this theorem, we can obtain that the ergodicity of Teichmüller geodesic flow implies that the Teichmüller
horocycle flow is ergodic and mixing (the latter one will imply the ergodicity of mapping class group action
on the space of measured foliations/laminations). We will prove the Howe-Moore theorem by considering
the unitary representations of simple Lie group G.
October 28, Axel Kodat, Distortion elements in diffeomorphism groups
November 4, Lucas Furtado, Local stable manifold of a smooth dynamical systems at a hyperbolic fixed point.
November 11, Yuan (Jessica) Liu, The unique measure of maximum entropy (MME) on the square-free flow.
November 18, Bryce Gollobit, Classification of infinite-dimension linear dynamics.
November 25, No event (Thanksgivings)
December 2, Lucas Furtado, Local stable manifold of a smooth dynamical systems at a hyperbolic fixed point, Part 2
December 9, Yuan (Jessica) Liu, The unique measure of maximum entropy (MME) on the square-free flow, Part 2
December 16, Final Exam Period