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