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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:

  1. Spectral Gap and Transience for Ruelle Operators on Countable Markov Shifts with Omri Sarig. Commun. Math. Phys. 292, 637-666 (2009).
  2. Countable Markov Shifts with Transient Potentials Proc. London Math. Soc. 103(6), 923-949 (2011).
  3. A Number Theoretic Question Arising in the Geometry of Plane Curves and Billiard Dynamics Proc. Amer. Math. Soc. 140, 3035-3040 (2012).
  4. Nonexpansive Z^2-subdynamics and Nivat’s conjecture with Bryna Kra, Trans. Amer. Math. Soc. 367, 6487-6537 (2015).
  5. Harmonic Labeling of Graphs with Itai Benjamini, Eviatar Procaccia, and Ran Tessler. Discr. Math. 313, 1726-1745 (2013).
  6. Complexity of short rectangles and periodicity with Bryna Kra, European J. Combin. 52, 146-173 (2016).
  7. The automorphism group of a shift of subquadratic growth with Bryna Kra, Proc. Amer. Math. Soc. 144, no. 2, 613-621 (2016).
  8. Complexity and directional entropy in two dimensions with Ryan Broderick and Bryna Kra, Israel J. Math. 215, 135-162 (2016).
  9. 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).
  10. Counting generic measures for a subshift of linear growth with Bryna Kra, J. Eur. Math. Soc., 21, no. 2, 355-380 (2019).
  11. The automorphism group of a minimal shift of stretched exponential growth with Bryna Kra, J. Mod. Dyn. 10, 483-495 (2016).
  12. Free ergodic Z^2-systems and complexity with Bryna Kra, Proc. Amer. Math. Soc. 145, no. 3, 1163-1173 (2017).
  13. The spacetime of a shift automorphism with John Franks and Bryna Kra, Trans. Amer. Math. Soc., no. 1, 461-488 (2019).
  14. Distortion and the automorphism group of a shift with John Franks, Bryna Kra, and Samuel Petite, J. Mod. Dyn. 13, 147-161 (2018).
  15. Positive entropy equilibrium states with Vaughn Climenhaga, Israel J. Math. 232, no. 2, 899-920 (2019).
  16. The automorphism group of a shift of slow growth is amenable with Bryna Kra, ETDS 40, no. 7, 1788-1804 (2020).
  17. Realizing ergodic properties in zero entropy subshifts with Bryna Kra, Israel J. Math. 240, 119-148 (2020).
  18. 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).
  19. The complexity threshold for the emergence of Kakutani inequivalence with Aimee Johnson, Bryna Kra, and Ayse Sahin, Israel J. Math. 251, 271-300 (2022).
  20. Characteristic measures for language stable subshifts with Bryna Kra, to appear in Monatsh. Math. 201, no. 3, 659-701 (2023).
  21. Strong approximation of shifts and the characteristic measures problem with Bryna Kra and Samuel Petite, to appear in Math. Z.
  22. Chaotic almost minimal actionswith Bryna Kra and Scott Schmieding, submitted.