Clayton Mizgerd

me

I'm a fourth year PhD student in mathematics at the University of Illinois Chicago. I am grateful to be advised by Vishesh Jain and Dhruv Mubayi. Before that, I got my B.A. in mathematics from Williams College. My research interests are generally in probability and combinatorics with applications in theoretical computer science. For summer 2025, I am grateful to be supported as an IDEAL fellow supervised by Will Perkins.

I am co-organizing the 2026 edition of the Graduate Student Combinatorics Conference on 03/27-03/29/2026. Please don't hesitate to reach out with any questions. We are excited to host you in Chicago!

In 2025-26, I am co-organizing UIC's Computer Science Theory Seminar with Shyam Ravichandran. In 2024-25, I co-organized UIC's Graduate Combinatorics, Algorithms, and Probability Seminar with Emily Cairncross.

Papers

  1. Optimal mixing of the inverse walk on the symmetric group, with Vishesh Jain. Submitted.
  2. The random graph process is globally synchronizing, with Vishesh Jain and Mehtaab Sawhney. Submitted. arXiv
  3. Inducibility of rainbow graphs, with Emily Cairncross, Dhruv Mubayi. Submitted. arXiv
  4. Rapid mixing of the down-up walk on matchings, with Vishesh Jain. APPROX/RANDOM 2024. arXiv
  5. Indeterminate cases of the Hamburger moment problem. Undergraduate senior thesis. link
  6. Critical points of the random cluster model with Newman-Ziff sampling, with Tolson Bell, Jerrell Cockerham, Christian Scullard, Melita Wiles. Journal of Physics A: Mathematical and Theoretical. arXiv
  7. Generalizing Zeckendorf's theorem to homogeneous linear recurrences II, with Thomas Martinez, Steven J. Miller, Jack Murphy, Chenyang Sun. Fibonacci Quarterly. arXiv
  8. Generalizing Zeckendorf's theorem to homogeneous linear recurrences I, with Thomas Martinez, Steven J. Miller, Chenyang Sun. Fibonacci Quarterly. arXiv
  9. Deterministic Zeckendorf games, with Ruoci Li, Xiaonan Li, Steven J. Miller, Chenyang Sun, Dong Xia, Zhyi Zhou. Fibonacci Quarterly. arXiv

Teaching

My office hours are listed on the MSLC website.

Outreach and Mentorship