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.
In Spring 2019 I am teaching Math 211 (Calculus III) and Math 212 (Differential Equations). Information for these courses is available on Moodle.
- 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., doi:10.4171/JEMS/838 (2018).
- 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., doi:10.1090/tran/7254 (2018).
- Distortion and the automorphism group of a shift with John Franks, Bryna Kra, and Samuel Petite, To appear in J. Mod. Dyn.
- Positive entropy equilibrium states with Vaughn Climenhaga, To appear in Israel J. Math.
- The automorphism group of a shift of slow growth is amenable with Bryna Kra, To appear in ETDS.
- Realizing ergodic properties in zero entropy subshifts with Bryna Kra, submitted.