# MSCS Seminars Today

## Calendar for Sunday February 18, 2018

Sunday February 18, 2018

**Chicago Action Now rotating workshop**

On stationary measure rigidity and orbit closures for actions of non-abelian groups

Alex Eskin (University of Chicago)

9:30 AM in SEO 636

I will describe joint work in progress with Aaron Brown, Federico Rodriguez-Hertz and Simion Filip. Our aim is to find some analogue, in the context of smooth dynamics, of Ratner's theorems on unipotent flows. This would be a (partial) generalization of the results of Benoist-Quint and my work with Elon Lindenstrauss in the homogeneous setting, the results of Brown and Rodriguez-Hertz in dimension 2, and my results with Maryam Mirzakhani in the setting of Teichmuller dynamics.

Tea at 9am

**Chicago Action Now rotating workshop**

Characterizing symmetric spaces by their Lyapunov spectra

Clark Butler (University of Chicago)

11:00 AM in SEO 636

We show that closed negatively curved locally symmetric spaces are characterized among nearby Riemannian manifolds by the Lyapunov spectra of the geodesic flow along periodic orbits. Our methods extend to locally characterize these geodesic flows by their Lyapunov spectra among nearby smooth flows. The main tools include the invariance principle for vanishing Lyapunov exponents and recent absolute continuity results in quasisymmetric mapping theory.

**Chicago Action Now rotating workshop**

A New Invariant in Complex Dynamics

Kenneth Jacobs (Northwestern University)

1:30 PM in SEO 636

Motivated by recent results in arithmetic dynamics, we will introduce a new invariant attached to a rational map f defined over the complex numbers. Its construction depends on an auxiliary equivariant -- a function on real hyperbolic 3 space -- which also appears to carry information about the dynamics of the map f. In this talk, we will discuss what is known about these objects, both in the setting of complex dynamics and in the setting of arithmetic dynamics.

**Chicago Action Now rotating workshop**

Generalizations of Furstenberg's diophantine result

Asaf Katz (University of Chicago)

3:00 PM in SEO 636

In his seminal paper from 1967, H. Furstenberg proved his famous x2x3 theorem which states that for every irrational x, the set 2^{n}3^{m}x is dense modulo 1.
I will show a couple of generalizations of this result, which imply density of sparser sequences, using earlier works of D. Meiri and M. Boshernitzan. In particular, I will show density modulo 1 of sequences such as 2^{n}3^{3^{m}}3^{3^{k^2}}x, for every irrational x.I will also discuss another result which is concerned with the case where no group action is present.
The talk will be accessible, no prior knowledge is assumed.