Jon Chaika

I am on leave at the IAS for the Fall 2025/Spring 2026 Academic year

Jon Chaika
University of Utah
Department of Mathematics
155 S 1400 E RM 233
Salt Lake City, UT, 84112-0090
USA
Email: chaika at math dot utah dot edu

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My papers on the arxiv
Summary of my papers

Papers


Tremors and horocycle dynamics on the moduli space of translation surfaces (with J. Smillie and B. Weiss) (accepted Annals of Math)

Weakly Mixing Polygonal Billiards (with G. Forni) (accepted Annals of Math)

Horocycle dynamics in rank one i> weak measure classification and equidistribution (with B. Weiss and F. Ygouf) (accepted Israel Journal of Mathematics>

On the Space of Ergodic Measures for the Horocycle Flow on Strata of Abelian Differentials (with O. Khalil and J. Smillie) (Annales scientifiques de l'ENS 2025)

On the ergodic theory of the real Rel foliation (with B. Weiss) (Forum math. Pi 2024)

Shrinking rates of horizontal gaps for generic translation surfaces (with S. Fairchild) (Geometriae Dedicata 2024)

Path-connectivity of the set of uniquely ergodic and cobounded foliations (with S. Hensel) (Geometriae Dedicata 2024)

Appendix A of Pairs in discrete with applications to Veech surfaces (Paper by C. Burrin and S. Fairchild) (Accepted Journal of the EMS)

Connectivity of the Gromov Boundary of the Free Factor Complex (with M. Bestvina and S. Hensel) (Annales Henri Lebesgue 2023)

Zero Measure Spectrum for Multi-Frequency Schrodinger Operators (with D. Damanik, J. Fillman and P. Gohlke) (Journal of Spectral Theory 2022)

A prime system with many self-joinings (with B. Kra) (Journal of Modern Dynamics 2021)

Self-Joinings for 3-IETs (with A. Eskin) (Journal of the EMS 2021)

Singularity of the spectrum for smooth area-preserving flows in genus two and translation surfaces well approximated by cylinders (with K. Frączek, A. Kanigowski, C. Ulcigrai) (Communications in Mathematical Physics 2021)

The set of non-uniquely ergodic d-IETs has Hausdorff codimension 1/2 (with H. Masur) (Inventiones Mathematicae 2020)

Ergodicity of skew products over linearly recurrent IETs (with D. Robertson) (Journal of the London Mathematical Society 2019)

A smooth mixing flow on a surface with non-degenerate fixed points (with A. Wright) (Journal of the AMS 2019)

Limits in PMF of Teichmuller geodesics (with H. Masur and M. Wolf) (Crelle's Journal 2019)

Stationary coalescing walks on the lattice (with A. Krishnan) (Probability Theory and Related Fields 2019)

Quantitative shrinking target properties for rotations, and interval exchanges (with D. Constantine) (Israel Journal of Mathematics 2019)

The set of uniquely ergodic IETs is path connected (with S. Hensel) (Ergodic Theory and Dynamical Systems 2019)

Uniform distribution of saddle connection lengths (with D. Robertson) (Journal of Modern Dynamics 2019)

Mobius disjointness for interval exchange transformations on three intervals (with A. Eskin) (Journal of Modern Dynamics 2019)

Circle averages and disjointness in typical flat surfaces on every Teichmuller disc (with P. Hubert) (Bulletin of the London Mathematical Society 2017)

Logarithmic laws and unique ergodicity (with R. Treviño) (Journal of Modern Dynamics 2017)

A dichotomy for arithmetic progressions in subsets of reals (with M. Boshernitzan) (Proceedings of the AMS 2016)

Appendix C of Right-angled billiards and volumes of moduli spaces of quadratic differentials on $\mathbb{C}P^1$ (paper by J. Athreya, A. Eskin and A. Zorich) (Annales scientifiques de l'ENS 2016)

The Hausdorff dimension of nonuinquely ergodic directions in H(2) is almost everywhere 1/2 (with J. Athreya) (Geometry and Topology 2015)

Every flat surface is Birkhoff and Osceledets generic in almost every direction (with A. Eskin) (Journal of Modern Dynamics 2015)

There exists an interval exchange with a non-ergodic generic measure (with H. Masur) (Journal of Modern Dynamics 2015)

Topological mixing for some residual sets of interval exchange transformations (with J. Fickenscher) (Communications in Mathematical Physics 2015)

The gap distribution of slopes on the golden L (with J. Athreya and S. Lelievre) (Contemporary Mathematics 2015)

Omega recurrence in cocycles (with D. Ralston) (Ergodic Theory and Dynamical Systems 2014)

Every transformation is disjoint from almost every non-classical exchange (with V. Gadre) (Geometriae Dedicata 2014)

Skew products over rotations with exotic properties (Geometriae Dedicata 2014)

Diophantine properties of IETs and general systems: Quantitative proximality and connectivity (with M. Boshernitzan) (Inventiones mathematicae 2013)

Winning games for bounded geodesics in Teichmueller discs (with Y. Cheung and H. Masur) (Journal of Modern Dynamics 2013)

Every transformation is disjoint from almost every IET (Annals of Mathematics 2012)

Borel-Cantelli Sequences (with M. Boshernitzan) (Journal d'Analyse Mathematique 2012)

The distribution of gaps for saddle connection directions (with J. Athreya) (Geometric and Functional Analysis 2012)

There exists a topologically mixing IET (Ergodic Theory and Dynamical Systems 2012)

Shrinking targets for IETs (Geometric and Functional Analysis 2011)

Schrödinger operators defined by interval exchange transformations (with D. Damanik and H. Krüger) (Journal of Modern Dynamics April 2009)

Hausdorff dimension for ergodic measures of interval exchange transformations (Journal of Modern Dynamics July 2008)

Veech Surfaces and Expanding Twist Tori on Moduli Spaces of Abelian Differentials (with O. Khalil) (submitted)

A rank one mild mixing system without minimal self joinings (with D. Robertson) (submitted)

Path-connectivity of Thick Laminations, and Markov Processes with Thick Limit Sets (with S. Hensel) (submitted)

The typical measure preserving transformation is not an interval exchange transformation (with D. Davis) (submitted)

Weak mixing in rational billiards (with F. Arana-Herrera and G. Forni) (submitted)

Ergodic homogeneous multidimensional continued fraction algorithms (with A. Nogueira)

On the Hausdorff dimensions of a singular ergodic measure for some minimal interval exchange transformations

The densest sequence in the unit circle (with M. Boshernitzan)

On the Frequency of Balanced Times in Cylinder Flows (with D. Ralston)

[0,1] is not a Minimality Detector for [0,1]^2

A theorem on accepted elasticity in certain local arithmetical congruence monoids (with M. Banister, S. Chapman and W. Meyerson) ( Abh. Math. Semin. Univ. Hambg. 2009)

On a result of James and Niven concerning unique factorization in congruence semigroups (with M. Banister, S. Chapman and W. Meyerson) (Elem. Math. 62 2007)

On the arithmetic of arithmetical congruence monoids (with M. Banister, S. Chapman and W. Meyerson) ( Colloq. Math. 2007)

On the Minkowski Diagonal Function for two real numbers. (with I. Kan and N. Moshchevitin) (Diophantine analysis and related fields 2011)



Online working seminar in ergodic theory
Max Dehn Seminar
Stochastics seminar
Wasatch topology conference
Evelyn Lamb

I was a co-organizer for an MRC program at snowbird in 2017. This is a great program.

A mathcircle I wrote on happy numbers and some thoughts.


Some things for visitors to Salt Lake City
Some restaurants, coffee shops and sights
Some hikes
I gratefully acknowledge the support of the NSF, and the Warnock fund. The views expressed here are of course my own.