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