Research

My areas of research are harmonic analysis and geometric measure theory. My ArXiv page is here, and my PhD thesis can be found here. 

Publications and preprints

1. Improved bound on the dimension of vertical projections in the Heisenberg group via intersections. (Preprint 2025)  ArXiv 

2. (with J. Green, Y. Ou, K. Ren, and S. Tammen) Incidence bounds related to circular Furstenberg sets.  (Preprint 2025)  ArXiv 

3. Exceptional sets for length under restricted families of projections onto lines in ℝ­3. (Preprint 2024) ArXiv 

4. (with J. Green and Y. Ou) An L3/2  SL2  Kakeya maximal inequality. (Preprint 2024) HAL preprint  

5. Vertical projections in the Heisenberg group for sets of dimension greater than 3. To appear in Indiana Univ. Math. J. ArXiv Journal 

6. Length of sets under restricted families of projections onto lines. Recent Developments in Harmonic Analysis and its Applications, 1–17. Contemp. Math., 792. American Mathematical Society, Providence, RI, 2024 ArXiv Journal 

7. (with S. Gan, S. Guo, L. Guth, D. Maldague, and H. Wang) On restricted projections to planes in ℝ­3.  To appear in Amer. J. Math.  ArXiv 

8. A Euclidean Fourier-analytic approach to vertical projections in the Heisenberg group. Bull. Lond. Math. Soc. 55 (2023), no. 2, 961-977. ArXiv Journal 

9. (with J. M. Fraser and N. G. Kroon) On the Fourier dimension of (d, k)-sets and Kakeya sets with restricted directions. Math. Z. 301 (2022), no. 3, 2497-2508. ArXiv Journal

10. Restricted families of projections onto planes: The general case of nonvanishing geodesic curvature. Rev. Mat. Iberoam. 39 (2023), no. 5, 1863-1894. ArXiv Journal

11. Low-dimensional pinned distance sets via spherical averages. J. Geom. Anal. 31 (2021), no. 11, 11410-11416. ArXiv Journal

12. (with A. Barron and M. B. Erdoğan) Fourier decay of fractal measures on hyperboloids. Trans. Amer. Math. Soc. 374 (2021), no. 2, 1041-1075. ArXiv Journal

13. (with C. N. Y. Huynh and F. Román-García) Dimension distortion by right coset projections in the Heisenberg group. J. Fractal Geom. 8 (2021), no. 4, 305-346. ArXiv Journal

14. Improved bounds for restricted projection families via weighted Fourier restriction. Anal. PDE 15 (2022), no. 7, 1655-1701. ArXiv Journal

15. An a.e. lower bound for Hausdorff dimension under vertical projections in the Heisenberg group. Ann. Acad. Sci. Fenn. Math. 45 (2020), no. 2, 723-737. ArXiv Journal

16. Improved decay of conical averages of the Fourier transform. Proc. Amer. Math. Soc. 147 (2019), no. 11, 4781-4796. ArXiv Journal

17. (with B. Kirchheim and C.-C. Lin) Two-by-two upper triangular matrices and Morrey's conjecture. Calc. Var. Partial Differential Equations 57 (2018), no. 3, Paper No. 73, 12 pp. ArXiv Journal

18. Upper semicontinuity of the lamination hull. ESAIM Control Optim. Calc. Var. 24 (2018), no. 4, 1503-1510. ArXiv Journal 

Other notes (not intended for peer-reviewed publication)

1. An L4/3  SL2  Kakeya maximal inequality. (superseded by hal-04386684) (2023) ArXiv

2. Fourier dimension of the cone. (subsumed in arXiv:2105.11414v2) (2021) ArXiv

3. Refined Strichartz inequalities for the wave equation. (superseded by arXiv:1806.08051v4) (2018) ArXiv

4. Differentiability of quasiconformal reflections (undergraduate summer research project). (2015) PDF