### Welcome to the online working seminar in ergodic theory

**A bit about the seminar:**

It meets weekly online usually on Mondays at** 9 am Utah time**.

Participants take turns presenting a paper, which hopefully admits a nice
one hour presentation.

This seminar is flexible, so if another time is better or one wishes to give a pre-talk to make it more accessible
that is great.

Talks from session 1 (with videos!)

**October 5**

Title:Equidistribution of geodesic flow pushes
via exponential mixing.

Abstract: Pick a point at random in a finite volume hyperbolic
surface and simultaneously flow in all directions from it.
For the typical starting point these expanding circles will
equidistribute and this talk will present
a (more general) argument of Margulis establishing this fact.

Speaker: Jon Chaika

Slides Note corrections are in red

Video

**October 12**

Title: A recurrence lemma and its applications and extensions

Abstract: I will discuss a lemma which is usually attributed to Atkinson, is very useful and apparently has been rediscovered multiple times. The lemma says that if (X, B, mu, T) is an ergodic system and f is in L^1(mu) with mean zero, then the Birkhoff sums of f do not diverge almost surely. Moreover the sums switch signs in a wide sense, infinitely many times. I will give the proof and discuss some applications of this result. Then I will discuss higher dimensional analogues, where the situation is significantly more complicated.

Speaker: Barak Weiss

Video link

**October 19**

Title: Measure rigidity of Cartan actions

Abstract: We'll take an introductory peek into the measure rigidity program for higher-rank abelian actions by looking at the simplest case, Anosov Z^k actions on (k+1)-dimensional tori. The main structures and ideas appearing in the theory will be explained, as well as how the situation becomes more complicated under fewer assumptions.

Speaker: Kurt Vinhage

Notes

**October 26**

Title: An invitation to "Entropy in Dimension One

Abstract: Which real numbers arise as the entropies of continuous, multimodal, postcritically finite self-maps of real intervals? This is the "one-dimensional" analogue of a more famous open question: which real numbers arise as the dilatations of pseudo-Anosov surface diffeomorphisms? In "Entropy in Dimension One," W. Thurston answers this one-dimensional version of the question. We'll discuss a small subset of the many beautiful ideas and questions in this paper.

Speaker: Kathryn Lindsey

**November 2**

Title: TBA

Speaker:
Jayadev Athreya