In this talk we will discuss substitution systems that have the property of minimal self-joinings. Then we will focus our attention on self-similar interval exchange transformations and their associated substitutions. We will show that 3-IETs have MSJ. This is joint with Giovanni Forni.

# Ergodic Theory & Statistical Mechanics

This weekly seminar welcomes many visiting speakers and also provides a forum for results by Princeton/IAS faculty and graduate students. While most talks focus on one of the two namesake topics, there tends to be overlap with other fields. Most recently, talks have included material on celestial mechanics, number theory, probability theory, the Schrodinger equation, spectral theory and Teichmueller theory.

For more information about this seminar, contact Yakov Sinai or Jon Fickenscher

**Please click on seminar title for complete abstract.**

##### Minimal Self-Joinings of Substitutions Arising from IETs

University of Maryland

##### TBA - Dmitry Zakharov

Courant Institute of Mathematical Sciences

##### TBA - David Aulicino

University of Chicago

##### Outer billiards and the plaid model

Outer billiards is a billiards-like dynamical system which is defined on the outside of a convex shape in the plane. Even for simple shapes, like kites (bilaterally symmetric quadrilaterals), the orbits have an intricate fractal-like structure.

Brown University