Kevin Ren

Department of Mathematics, Princeton University

Email: kevinren [at] princeton [dot] edu

I am a fourth year graduate student at Princeton University, advised by Assaf Naor.

I study the multiscale structure of geometric objects, leveraging key insights to prove new results in geometric analysis and algorithm design.

Here is my CV (updated Sept 2025).

Here is a talk and article about my work on the Furstenberg set problem.

Here is an article about my work on the Falconer distance set problem.

I am grateful to be supported by the NSF Graduate Research Fellowship, the Simons Dissertation Fellowship for Mathematics, and the Cubist PhD Fellowship.


Publications and preprints

Analysis and Geometric Measure Theory

  1. Incidence bounds related to circular Furstenberg sets (joint with John Green, Terence L. J. Harris, Yumeng Ou, Sarah Tammen).
  2. Euclidean embedding, randomized clustering, and Lipschitz extension for finite and doubling subsets of L_p when p > 2 (joint with Assaf Naor).
  3. Random zero sets with local growth guarantees (joint with Alan Chang, Assaf Naor). STOC '25: Proceedings of the 57th Annual ACM Symposium on Theory of Computing. full version
  4. On the projections of almost Ahlfors regular sets (joint with Tuomas Orponen).
  5. Radial Projections in R^n Revisited (joint with Paige Bright and Yuqiu Fu).
  6. Sobolev extension in a simple case (joint with Marjorie Drake, Charles Fefferman, and Anna Skorobogatova). Advanced Nonlinear Studies 25 (2025), no. 2, pp. 260-278
  7. Weighted refined decoupling estimates and application to Falconer distance set problem (joint with Xiumin Du, Yumeng Ou, and Ruixiang Zhang).
  8. New improvement to Falconer distance set problem in higher dimensions (joint with Xiumin Du, Yumeng Ou, and Ruixiang Zhang).
  9. Discretized Radial Projections in R^d.
  10. Furstenberg sets estimate in the plane (joint with Hong Wang).
  11. A note on maximal operators for the Schrödinger equation on the torus (joint with Yuqiu Fu, Haoyu Wang).
  12. Incidence estimates for alpha-dimensional tubes and beta-dimensional balls in the plane (joint with Yuqiu Fu). J Fractal Geometry 11 (2024), no. 1/2, pp. 1–30
  13. An incidence estimate and a Furstenberg type estimate for tubes in the plane (joint with Yuqiu Fu and Shengwen Gan). J Fourier Anal Appl 28, 59 (2022)

Combinatorics

  1. %-Immanants and Temperley-Lieb Immanants (joint with Frank Lu, Dawei Shen, Siki Wang).
  2. Topology of Augmented Bergman Complexes (joint with Elisabeth Bullock, Aidan Kelley, Victor Reiner, Gahl Shemy, Dawei Shen, Brian Sun, Amy Tao, Zhichun Joy Zhang). Electronic Journal of Combinatorics, p. 1-31 (2022)
  3. Extending the Graph Formalism to Higher-Order Gates (joint with Andrey Boris Khesin). Quantum Inf. Comput. 23 (2023), no. 13-14, 1128–1141.

arxiv page

ORCID 0000-0001-8348-022X


Invited talks