RESEARCH
RESEARCH
My research interests are primary in dynamical systems and ergodic theory. I study the thermodynamic formalism of non-uniformly hyperbolic dynamical systems. In particular, my doctoral work was on transfer operator theory for nonstationary dynamical systems. While continuing this research during my postdoc, I have also expanded my scope to include projects on mixing rates for geodesic flow on negatively curved surfaces and equilibrium states for systems that exhibit both hyperbolic and elliptic behavior.
My research is supported by the following grants:
2023-2026: NSF DMS-2316687 "MPS-ASCEND: Equilibrium States for Non-stationary Dynamical Systems"
2020-2022: AGEP-GRS Supplement to NSF DMS-1554794 "CAREER: Unifying approaches to non-uniform hyperbolicity"
Conjugacies for Expanding Skew Products on 𝕋n
submitted (2025)
Equilibrium States for Non-uniformly Expanding Skew Products
published in Ergodic Theory and Dynamical Systems (2023)
Nonstationary Ruelle-Perron-Frobenius Theorem
Joint with V. Climenhaga (UH) (expected 2025)
Equilibrium States on Expanding Skew Products
approved dissertation from University of Houston (2023)
Shift Spaces with Specification are Intrinsically Ergodic
Master's Thesis from University of Houston
Upcoming:
"Thermodynamic Formalism of Special Billiard Flows", 7/28/25 - 8/1/25
Dynamics, Networks, and Complex Systems Mini-symposium
at The Third Joint SIAM/CAIMS Annual Meetings (AN25)
Past:
"Equilibrium States for the Standard Map" (Short, Slides), 5/2/25 (Cancelled)
ASCEND Mentor Network Fellowship Conference, San Diego, CA,
"Conjugacies of Expanding Skew Products" (Short, Slides), 4/3/25
Workshop on Dynamical Systems and Related Topics at the University of Maryland
"An Application of Nonstationary Measures for Expanding Skew Products", 1/11/25
Workshop on Statistical Properties of Smooth Dynamical Systems at Wake Forest University
"Nonstationary Measures for some Expanding Skew Products", 10/31/24
Dynamics Seminar at Indiana University at Indianapolis
"Nonstationary Measures for some Expanding Skew Products", 10/16/24
Ergodic Theory Seminar at The Ohio State University
"A Glimpse into Thermodynamic Formalism" (Short), 10/10/24
ASCEND Mentor Network Fellowship Conference, Nashville, TN
"Equilibrium States for Non-uniformly Expanding Skew Products", 03/05/24
RTG Dynamics Seminar at Northwestern University
"Equilibrium States for Non-uniformly Expanding Skew Products", 11/8/23
Dynamics Learning Seminar at The Ohio State University
"Equilibrium States for Expanding Skew Products" (Short), 05/21/22
Houston Workshop on Hyperbolic Dynamical Systems at the University of Houston