Research

Preprints and Publications

Dynamical Systems

1. Completely parabolic surfaces are Veech [pdf][arXiv], 2pp., October 2026.

2. Cusp excursions, lattice points on manifolds, and the Mizohata-Takeuchi conjecture [pdf][arXiv], 38pp., June 2026. Submitted.

Harmonic Analysis

1. Sharp lower bounds for the periodic maximal Schrödinger operator in higher dimensions (joint with Taylor Tan) [pdf][arXiv], 11pp., September 2026. 10 pages.

2. Maximal estimates for perturbations of the Schrödinger operator on tori (joint with Taylor Tan) [pdf][arXiv], 18pp., August 2026.

Miscellaneous

1. Subvarieties without absolute saddle connections [pdf]. October 2026.

2. Furstenberg's conjecture for polynomially rich semigroups [pdf]. July 2023.

3. Spectral data in finite quotients [pdf]. September 2025.

4. Mapping class group fixed representations [pdf]. June 2025.

5. Invariant sets of multidimensional tori (undergraduate thesis) [pdf]. April 2023.

6. Translation surfaces: from rotations on the circle to horocycle flow (lecture notes from a minicourse led by Jon Chaika) [pdf]. June 2025.

7. A counterexample for the exact periodic Schrodinger maximal operator (ChatGPT output) [pdf]. September 2026.