Kevin Ren

he/him pronouns

Department of Mathematics, Princeton University

Email: kevinren [at] princeton [dot] edu

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

I am interested in studying Fourier analysis and its applications to problems in geometric measure theory and metric geometry.

Here is my CV (updated Feb 2024).

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.


Publications and preprints

Analysis and Geometric Measure Theory

  1. Sobolev extension in a simple case (joint with Marjorie Drake, Charles Fefferman, and Anna Skorobogatova). Accepted by Advanced Nonlinear Studies
  2. Weighted refined decoupling estimates and application to Falconer distance set problem (joint with Xiumin Du, Yumeng Ou, and Ruixiang Zhang).
  3. New improvement to Falconer distance set problem in higher dimensions (joint with Xiumin Du, Yumeng Ou, and Ruixiang Zhang).
  4. Discretized Radial Projections in R^d.
  5. Furstenberg sets estimate in the plane (joint with Hong Wang).
  6. A note on maximal operators for the Schrödinger equation on the torus (joint with Yuqiu Fu, Haoyu Wang).
  7. Incidence estimates for alpha-dimensional tubes and beta-dimensional balls in the plane (joint with Yuqiu Fu). Accepted by J Fractal Geometry
  8. 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).

arxiv page

ORCID 0000-0001-8348-022X


Invited talks