Research

Research interests

Smooth Dynamical Systems, Ergodic Theory, the interplay between Dynamics, Geometry and Spectral Theory.

Publications

  1. Unique equilibrium states for geodesic flows on flat surfaces with singularities (with Benjamin Call, David Constantine, Noelle Sawyer, and Grace Work)- ArXiv: 2101.11806
  2. Riemannian Anosov extension and applications (with Dong Chen and Andrey Gogolev) – ArXiv: 2009.13665
  3. Flexibility of Lyapunov exponents with respect to two classes of measures on the torus – to appear in Ergod. Th. & Dynam. Sys., Anatole Katok Memorial Volume
  4. Geometry and entropies in a fixed conformal class on surfaces (with Thomas Barthelmé) – to appear in Annales de l’Institut Fourier
  5. Exceptional directions for the Teichmüller geodesic flow and Hausdorff dimension (with Hamid Al-Saqban, Paul Apisa, Osama Khalil, Shahriar Mirzadeh, and Caglar Uyanik) – J. Eur. Math. Soc. (JEMS), Vol. 23, Issue 5, 2021, 1423-1476.
  6. Flexibility of entropies for surfaces of negative curvature (with Anatole Katok) – Isr. J. Math.,  Vol. 232, Issue 2, 2019, 631-676.
  7. Flexibility of Lyapunov exponents for expanding circle maps – Discrete Contin. Dyn. Syst., Vol. 39 (5), 2019, 2325-2342
  8. Flexibility of geometric and dynamical data in fixed conformal classes (with Thomas Barthelmé) – Indiana Univ. Math. J., Vol. 69, No. 2, 2020, 513-540.
  9. Lyapunov Reducibility of Infinitesimal Perturbations of Equations and Systems, J. Math. Sci., Vol. 210, 2 (October, 2015), 200-209. (Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 30, Part I (2014) 145-160)