Clayton Mizgerd

I'm a fourth year PhD student in mathematics at the University of Illinois Chicago. I am fortunate 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. I am grateful to be supported by a Simons Dissertation Fellowship.

For summer 2025, I am grateful to be supported as an IDEAL fellow supervised by Will Perkins.

Papers

  1. How Fast does the Inverse Walk Approximate a Random Permutation?, with Vishesh Jain, Tianren Liu, Angelos Pelecanos, Stefano Tessaro, and Vinod Vaikuntanathan. 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. To appear in Mathematical Proceedings of the Cambridge Philosophical Society. 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, Melita Wiles, Christian Scullard. 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 Service