Papers

Research papers

Google scholar profile, ORCID profile

1. Random zero sets with local growth guarantees, preprint

   • with Assaf Naor, Kevin Ren

   • An extended abstract announcing parts of the algorithmic aspects of this work, and titled "Optimal rounding for Sparsest Cut," will appear in STOC 2025.

2. Prescribed projections and efficient coverings by curves in the plane, preprint

   • with Alex McDonald, Krystal Taylor

3. A random line intersects S^2 in two probabilistically independent locations, J. Geom. Anal. 35, 263 (2025).

   • with Dmitriy Bilyk, Otte Heinävaara, Ryan Matzke, Stefan Steinerberger

4. Nikodym sets and maximal functions associated with spheres, Rev. Mat. Iberoam. 41 (2025), no. 3, 1009–1056.

   • with Georgios Dosidis, Jongchon Kim

5. Structure of sets with nearly maximal Favard length. Anal. PDE 17 (2024), no. 4, 1473–1500.

   • with Damian Dąbrowski, Tuomas Orponen, Michele Villa

6. Decoupling for fractal subsets of the parabola. Math. Z. 301 (2022), no. 2, 1851–1879.

   • with Jaume de Dios, Rachel Greenfeld, Asgar Jamneshan, Zane Kun Li, José Madrid

7. Analytic capacity and projections. J. Eur. Math. Soc. 22 (2020), 4121-4159.

   • with Xavier Tolsa

   • 30-minute talk

8. Small unions of affine subspaces and skeletons via Baire category. Adv. Math. 328 (2018), 801–821.

   • with Marianna Csörnyei, Kornélia Héra, Tamás Keleti

9. The Kakeya needle problem and the existence of Besicovitch and Nikodym sets for rectifiable sets. Proc. London Math. Soc. 118 (2019), 1084-1114.

   • with Marianna Csörnyei

   • 50-minute talk (in Spanish)

10. The Whitney extension theorem in high dimensions. Rev. Mat. Iberoam. 33 (2017), no. 2, 623–632.

11. Newman's conjecture in function fields. J. Number Theory 157 (2015), 154–169.

    • with David Mehrle, Steven J. Miller, Tomer Reiter, Joseph Stahl, Dylan Yott

12. Newman's conjecture in various settings. J. Number Theory 144 (2014), 70–91.

    • with Julio Andrade, Steven J. Miller

    • 20-minute talk

Co-authors

1. Julio Andrade

2. Dmitriy Bilyk

3. Marianna Csörnyei

4. Damian Dąbrowski

5. Jaume de Dios Pont

6. Georgios Dosidis

7. Rachel Greenfeld

8. Otte Heinävaara

9. Kornélia Héra

10. Asgar Jamneshan

11. Tamás Keleti

12. Jongchon Kim

13. Zane Kun Li

14. José Ramón Madrid Padilla

15. Ryan Matzke

16. Alex McDonald

17. David Mehrle

18. Steven J. Miller

19. Assaf Naor

20. Tuomas Orponen

21. Tomer Reiter

22. Kevin Ren

23. Joseph Stahl

24. Stefan Steinerberger

25. Krystal Taylor

26. Xavier Tolsa

27. Michele Villa

28. Dylan Yott

Expository papers

1. Constructions of planar Besicovitch sets - My topic proposal for the 2nd year of the Ph.D. program.

2. Aleksandrov's theorem: closed surfaces with constant mean curvature - My final project for Amie Wilkinson's spring 2015 course on Riemannian geometry. My advisor for this project was Luis Silvestre.

3. On the Jones polynomial and its applications - My junior paper for the spring 2013 semester. My advisor was Zoltán Szabó. I turned this paper into the power round for PUMaC 2013 (see Outreach).

4. An overview of the Hamilton-Jacobi equation - My junior paper for the fall 2012 semester. My advisor was Peter Constantin. This paper discusses Hamiltonian mechanics, symplectic geometry, first-order nonlinear PDE theory, optimal control theory, and viscosity solutions.

Other writing

1. Advice on teaching at a new institution - I wrote this for the Notices of the AMS (June/July 2024) Early Career Section.

2. Finding and Creating Community in Your Department - Rachel Greenfeld and I wrote this for the Notices of the AMS (September 2024) Early Career Section.