Dept Banner
Dept Banner


Download as iCal file


Ergodic theory and the geometry of high-dimensional metric spaces

Tim Austin: Courant Institute

Location:  Hill 705
Date & time: Friday, 03 March 2017 at 4:00PM - 4:11PM

The most basic examples of shift-systems with positive entropy are the Bernoulli shifts, under which the coordinates are independent. In the special case of Bernoulli shifts, it was shown by Ornstein that entropy is actually a complete invariant. In order to prove this, Ornstein developed a concrete necessary and sufficient condition for a general shift-system to be isomorphic to a Bernoulli shift. We also know that Bernoulli shifts often appear as images of other, more complex systems under equivariant maps: by a theorem of Sinai, this is true whenever the necessary inequality between their entropies is satisfied.

The proofs of these more advanced results requires a delicate investigation of the finite-dimensional marginals of the shift-system, regarded as a sequence of discrete probability spaces endowed with their Hamming metrics. It turns out that other ergodic theoretic consequences are related to open problems on the possible structure of such discrete `metric probability spaces'. After sketching the history of this area, I will describe some of these connections.

This talk will require a knowledge of basic real analysis and some measure theory, and some simple probability theory will be helpful. I will not assume anything from dynamics or ergodic theory.

Special Note to All Travelers

Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.

Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.

Contact Us

HillCenter small

Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530