Here are a collection of papers and presentations I’ve done over the years.
Accepted
A counterexample to marked length spectrum semi-rigidity (with Andrey Gogolev) [2024]
Given a closed orientable negatively curved Riemannian surface, we show how to construct a perturbation such that each closed geodesic becomes longer, and yet there is no diffeomorphism which contracts every tangent vector. To appear in Groups, Geometry, and Dynamics.
Magnetic flatness and E. Hopf's theorem for magnetic systems (with Valerio Assenza and Ivo Terek) [2024]
Using the notion of magnetic curvature recently introduced by the first author, we extend E. Hopf's theorem to the setting of magnetic systems and study the notion of "magnetic flatness." To appear in Communications in Mathematical Physics.
A positive proportion Livshits theorem (with Caleb Dilsavor) [2024]
A generalization of the Livshits theorem using statistical information on orbits. Proceedings of the American Mathematical Society, (152) 11, 4729 - 4744 (2024).
Codazzi tensor fields in reductive homogeneous spaces (with Ivo Terek) [2023]
An extension of results by d'Atri on Codazzi tensors in the setting of reductive homogeneous spaces. Results in Mathematics (4) 79, 137.
Deformative Magnetic Marked Length Spectrum Rigidity [2022]
A generalization of Guillemin-Kazhdan to the setting of magnetic flows. Bulletin of the London Mathematical Society, (6) 55, 3077 - 3096 (2023). See the arXiv link above for a correction.
Submitted
TBD
Unpublished
Marked length spectrum rigidity for Anosov magnetic surfaces (with Valerio Assenza, Jacopo de Simoi, and Ivo Terek) [2024]
A generalization of Guillarmou, Lefeuvre, and Paternain to the setting of Anosov magnetic flows.
Anosov magnetic flows on surfaces (with Yumin Shen) [2023]
Using the quotient bundle introduced by Wojtkowski, we give necessary and sufficient conditions for a magnetic flow on a closed, oriented surface to be Anosov (part of the OSU Cycle Program).
Mixing Times of Random Walks on Various Combinatorial Objects [2018]
A write up for my REU during the summer of 2018.
Benford's Law and Voter Fraud [2016]
A short article I worked on my sophomore year on Benford's law and voter fraud. I worked on the code.
A Survey on Continuum Random Trees For Undergraduates [2016]
A short survey on the continuum random tree I wrote as a Freshman.
Presentations
Marked Length Spectrum Rigidity [2024]
Given at the OSU Ergodic Theory Seminar.
A counterexample to a marked length spectrum semi-rigidity problem (3) [2024]
A poster for the NUET Summer School at Northwestern.
Marked Length Spectrum Rigidity [2024]
Given at the Dynamical Systems Working Seminar at Penn State.
A counterexample to a marked length spectrum semi-rigidity problem (2) [2024]
Given at the semi-annual Workshop on Dynamical Systems and Related Topics at Maryland.
A Magnetic Hopf Theorem [2024]
Given at the "Dynamics Students Days" workshop in Maryland.
Geodesic Flows [2024]
A series of talks introducing the geodesic flow. Given at the OSU student dynamics seminar.
A counterexample to a marked length spectrum semi-rigidity problem [2023]
My presentation for the dynamics seminar at UChicago.
A counterexample to marked length spectrum semi-rigidity [2023]
A poster for the semi-annual Workshop in Dynamical Systems and Related Topics at Penn State.
The Hopf Theorem and Anosov flows [2023]
Given at the OSU student dynamics seminar.
Deformative Magnetic Marked Length Spectrum Rigidity (2)[2023]
My presentation for the Purdue Geometry and Geometric Analysis seminar.
A positive proportion Livshits theorem (2) [2023]
Given at the Northwestern summer school on dynamical systems.
A positive proportion Livshits theorem [2023]
Given at the Maryland summer school on partially hyperbolic systems.
Livshits' theorem and its generalizations [2023]
Given at the OSU student dynamics seminar.
Entropy rigidity [2023]
Given at the OSU student geometry, topology, and dynamics seminar.
The Weil-Petersson metric [2022]
Given at the OSU metric geometry/GGT student seminar.
Deformative Magnetic Marked Length Spectrum Rigidity [2022]
Given at the IUPUI ergodic theory seminar.
Marked length spectrum rigidity [2022]
Given at the Midwest dynamical systems early career conference.
Livshits' theorem and its applications [2021]
Given at the OSU student analysis seminar.
Dynamical coherence [2021]
Given at the OSU smooth ergodic theory student seminar.
Geodesic Flow and the Hopf Argument [2020]
My presentation for the OSU Ergodic Theory and Combinatorial Number Theory seminar . The presentation follows Einsiedler and Ward