Here are a collection of papers and presentations I’ve done over the years.
Accepted
Deformative Magnetic Marked Length Spectrum Rigidity [2022]
A generalization of Guillemin-Kazhdan to the setting of magnetic flows. To appear in the Bulletin of the London Mathematical Society.
A positive proportion Livshits theorem (with Caleb Dilsavor) [2023]
A generalization of the Livshits theorem using statistical information on orbits. To appear in the Proceedings of the American Mathematical Society.
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. To appear in Results in Mathematics.
Submitted
A counterexample to marked length spectrum semi-rigidity (with Andrey Gogolev) [2023]
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.
Unpublished
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 did most of the work 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 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
Markov Chains, Mixing Times, and Couplings (2) [2018]
My presentation for AISC at UNC Greensboro.
Markov Chains, Mixing Times, and Couplings [2018]
My presentation for the Indiana University REU conference.
Methods for Improving the Lower Bound of R(5,5) [2017]
My presentation for the 2017 Chicago MathFest.