## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Simplicity of the Lyapunov spectrum via Boundary theory

**Speaker:** Alex Furman

**Speaker Info:** University of Illinois, Chicago

**Brief Description:**

**Special Note**:

**Abstract:**

Consider products of matrices in $G=SL(d,R)$ that are chosen using
some ergodic dynamical system.
The Multiplicative Ergodic Theorem (Oseledets) asserts that the
asymptotically such products behave as $\exp(n\Lambda)$ where $\Lambda$
is a fixed diagonal traceless matrix, called the Lyapunov spectrum of
the system.
The spectrum $\Lambda$ depends on the system in a mysterious way, and
is almost never known explicitly.
The best understood case is that of random walks, where by the work of
Furstenberg, Guivarc'h-Raugi, and Gol'dsheid-Margulis we know that the
spectrum is simple (i.e. all values are distinct) provided the random
walk is not trapped in a proper algebraic subgroup.
Recently, Avila and Viana proved a conjecture of Kontsevich-Zorich
that asserts simplicity of the Lyapunov spectrum for another system
related to the Teichmuller flow.

**Date:** Tuesday, April 14, 2015

**Time:** 4:00pm

**Where:** Lunt 104

**Contact Person:** Prof. Bryna Kra

**Contact email:** kra@math.northwestern.edu

**Contact Phone:** 847-491-5567

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