 
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
    
        - 
            Incidence bounds related to circular Furstenberg sets
            (joint with John Green, Terence L. J. Harris, Yumeng Ou, Sarah Tammen).
        
- 
            Euclidean embedding, randomized clustering, and Lipschitz extension for finite and doubling subsets of L_p when p > 2
            (joint with Assaf Naor).
        
- 
            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
            
        
- 
            On the projections of almost Ahlfors regular sets
            (joint with Tuomas Orponen).
        
- 
            Radial Projections in R^n Revisited
            (joint with Paige Bright and Yuqiu Fu).
        
- 
            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
        
- 
            Weighted refined decoupling estimates and application to Falconer distance set problem
            (joint with Xiumin Du, Yumeng Ou, and Ruixiang Zhang).
        
- 
            New improvement to Falconer distance set problem in higher dimensions
                (joint with Xiumin Du, Yumeng Ou, and Ruixiang Zhang).
        
- 
            Discretized Radial Projections in R^d.
        
- 
            Furstenberg sets estimate in the plane (joint with Hong Wang).
        
- 
            A note on maximal operators for the Schrödinger equation on the torus
            (joint with Yuqiu Fu, Haoyu Wang).
        
- 
            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
        
- 
             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
    
    
        - 
            %-Immanants and Temperley-Lieb Immanants
            (joint with Frank Lu, Dawei Shen, Siki Wang).
        
- 
            
                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)
        
- 
            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
    
        - 
            Brin MRC Workshop on Sparse Equidistribution, Sept 2025
        
- 
            AIM Workshop on Metric Embeddings, July 2025
        
- 
            ACM Symposium on Theory of Computing, June 2025
        
- 
            MIT Analysis Seminar, Apr 2025
        
- 
            NYU Analysis Seminar, Feb 2025
        
- 
            Princeton Analysis Seminar, Feb 2025
        
- 
            University of North Carolina Analysis Seminar, Oct 2024
        
- 
            Northwestern Analysis Seminar, Apr 2024
        
- 
            AMS Spring Central Sectional Meeting, Apr 2024
        
- 
            UCLA Department Colloquium, Apr 2024
        
- 
            UPenn Analysis Seminar, Feb 2024
        
- 
            Workshop in Analysis at Georgia Institute of Technology, Dec 2023
        
- 
            Berkeley Analysis Seminar, Oct 2023
        
- 
            University of British Columbia Analysis Seminar, Oct 2023
        
- 
            Online Analysis Research Seminar, Sept 2023
        
- 
            Harmonic Analysis and Fractal Sets conference at Ohio State University, Mar 2023
        
- 
            Princeton Graduate Student Seminar, Oct 2022
        
- 
            Joint Mathematics Meetings AMS/PME student poster session, Jan 2022