My areas of research are in ergodic theory and dynamical systems. In particular, I am interested in studying Wiener-Wintner-type averages, weighted ergodic averages and the return times theorem, multiple ergodic averages, topological dynamics, thermodynamic formalism, fractal geometry, multifractal analysis, as well as partially hyperbolic systems.
(with I. Assani and J. Folks) "Higher order Wiener-Wintner systems: Examples and applications" (To appear in Acta. Math. Hungar.)
(with F. Micena, J. Rodriguez Hertz, and R. Ures) "Measures of maximal entropy that are SRB" (To appear in Advances in Mathematics)
(with Z. Buczolich and B. Maga) "Generic Birkhoff Spectra." Discrete & Continuous Dynamical systems. 40 (2020) no. 4, 6649-6679. DOI: 10.3934/dcds.2020131 https://www.aimsciences.org/article/doi/10.3934/dcds.2020131
(with I. Assani) "Extension of Wiener-Wintner double recurrence theorem to polynomials." Journal d'Analyse Mathématique 134 (2018), no. 2, 597-613. URL/DOI: https://doi.org/10.1007/s11854-018-0019-x
(with I. Assani) "A good universal weight for nonconventional ergodic averages in norm." Ergodic Theory and Dynamical Systems 37 (2017), no. 4, 1009-1025. URL/DOI: https://doi.org/10.1017/etds.2015.76
(with I. Assani and D. Duncan) "Pointwise characteristic factors for Wiener-Wintner double recurrence theorem." Ergodic Theory and Dynamical Systems 36 (2016) no. 4, 1037-1066. URL/DOI: https://doi.org/10.1017/etds.2014.99
"Multiple recurrence along a double return times sequence" (in preparation)
(with I. Cipriano) "Δ-transitivity for several transformations and an application to the coboundary problem."
Extensions of J. Bourgain's Double Recurrence Theorem. Thesis (Ph.D.)–The University of North Carolina at Chapel Hill. 2016. 89 pp. ISBN: 978-1339-81005-8 . Supervisor: Idris Assani
Roots of the Wronskian of Consecutive Hermite Polynomals. Undergraduate Honors Thesis. The University of Oregon. 2011. Advisor: Chris Sinclair.