I am an Associate Professor in the Department of Mathematics at Bucknell University. I work in dynamical systems and my recent interests have been studying the automorphisms and ergodic theory of zero entropy symbolic systems. I am also interested in thermodynamic formalism as well as problems related to multidimensional symbolic dynamics. My CV is available here.

#### Teaching:

In Spring 2024, I will be teaching Differential Equations (Math 212) and Real Analysis I (Math 308). Information for both courses is available on Moodle.

#### Papers:

**Spectral Gap and Transience for Ruelle Operators on Countable Markov Shifts**with Omri Sarig. Commun. Math. Phys. 292, 637-666 (2009).**Countable Markov Shifts with Transient Potentials**Proc. London Math. Soc. 103(6), 923-949 (2011).**A Number Theoretic Question Arising in the Geometry of Plane Curves and Billiard Dynamics**Proc. Amer. Math. Soc. 140, 3035-3040 (2012).**Nonexpansive Z^2-subdynamics and Nivat’s conjecture**with Bryna Kra, Trans. Amer. Math. Soc. 367, 6487-6537 (2015).**Harmonic Labeling of Graphs**with Itai Benjamini, Eviatar Procaccia, and Ran Tessler. Discr. Math. 313, 1726-1745 (2013).**Complexity of short rectangles and periodicity**with Bryna Kra, European J. Combin. 52, 146-173 (2016).**The automorphism group of a shift of subquadratic growth**with Bryna Kra, Proc. Amer. Math. Soc. 144, no. 2, 613-621 (2016).**Complexity and directional entropy in two dimensions**with Ryan Broderick and Bryna Kra, Israel J. Math. 215, 135-162 (2016).**The automorphism group of a shift of linear growth: beyond transitivity**with Bryna Kra, Forum of Mathematics, Sigma, 3, e5, doi: 10.1017/fms.2015.3 (2015).**Counting generic measures for a subshift of linear growth**with Bryna Kra, J. Eur. Math. Soc., 21, no. 2, 355-380 (2019).**The automorphism group of a minimal shift of stretched exponential growth**with Bryna Kra, J. Mod. Dyn. 10, 483-495 (2016).**Free ergodic Z^2-systems and complexity**with Bryna Kra, Proc. Amer. Math. Soc. 145, no. 3, 1163-1173 (2017).**The spacetime of a shift automorphism**with John Franks and Bryna Kra, Trans. Amer. Math. Soc., no. 1, 461-488 (2019).**Distortion and the automorphism group of a shift**with John Franks, Bryna Kra, and Samuel Petite, J. Mod. Dyn. 13, 147-161 (2018).**Positive entropy equilibrium states**with Vaughn Climenhaga, Israel J. Math. 232, no. 2, 899-920 (2019).**The automorphism group of a shift of slow growth is amenable**with Bryna Kra, ETDS 40, no. 7, 1788-1804 (2020).**Realizing ergodic properties in zero entropy subshifts**with Bryna Kra, Israel J. Math. 240, 119-148 (2020).**Boshernitzan’s condition, factor complexity, and an application**with Bryna Kra, Proc. Amer. Math. Soc., Ser. B, 9, 95-110, doi.org/10.1090/bproc/90 (2022).**The complexity threshold for the emergence of Kakutani inequivalence**with Aimee Johnson, Bryna Kra, and Ayse Sahin, Israel J. Math. 251, 271-300 (2022).**Characteristic measures for language stable subshifts**with Bryna Kra, to appear in Monatsh. Math. 201, no. 3, 659-701 (2023).**Strong approximation of shifts and the characteristic measures problem**with Bryna Kra and Samuel Petite, submitted.**Chaotic almost minimal actions**with Bryna Kra and Scott Schmieding, submitted.