ABOUT ME
My name is Polina Baron. I am a graduate student at the Department of Mathematics at the University of Chicago, projected to graduate in Spring 2026. I enjoy the honour of working with Professor Simion Filip. Before that, I did my Bachelour degree in Mathematics at HSE (Moscow, Russia; 2016-2020), where I was lucky to work under the guidance of Professor Alexandra (Sasha) Skripchenko. I am currently interested in Dynamical Systems and their applications. I also have side project in Integrable Systems.
To contact me, please write to pbaron at uchicago.edu
PREPRINTS AND PROJECTS
SPECTRAL AND MIXING PROPERTIES OF INTERVAL EXCHANGE TRANSFORMATIONS WITH FLIPS
(Bachelour's thesis, supervised by Sasha Skripchenko)
2020
We study interval exchange transformations with flips, which are piecewise isometries of an interval to itself with a finite number of jump discontinuities such that each of these isometries reverses the orientation of at least one of the intervals of continuity (called a flip). Unlike in the case of interval exchange transformations without flips, which are well-studied, many ergodic properties of interval exchange transformations with flips are yet to be discovered. In 2019, we have constructed an ergodic measure on the set of minimal interval exchange transformations with flips on 4 subintervals, namely the measure of maximal entropy. In this paper, we prove two following results:
Any interval exchange transformation with flips without a periodic point is not mixing with respect to any invariant Borel probability measure on it.
Almost all, with respect to the measure of maximal entropy on the set of them, minimal interval exchange transformations with flips on 4 subintervals are uniquely ergodic.
INVARIANT MEASURE FOR MINIMAL INTERVAL EXCHANGE TRANSFORMATIONS WITH FLIPS ON 4 INTERVALS
(supervised by Sasha Skripchenko)
2019
In this paper we study the invariant measures for minimal interval exchange transformations with flips. We construct the Rauzy diagram for minimal interval exchange transformations with flips in case of 4 subintervals. We introduce the roof function on the parameter space and provethe existence of the measure of maximal entropy for the suspension flow.