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.

Papers

  1. Equality in Fill's spectral gap problem, with Vishesh Jain. Submitted.
  2. Sampling Colorings Close to the Maximum Degree: Non-Markovian Coupling and Local Uniformity, with Vishesh Jain and Eric Vigoda. Submitted.
  3. On the chromatic number of random triangle-free graphs, with Will Perkins and Yuzhou Wang. Accepted to Random Structures & Algorithms.
  4. How Fast does the Inverse Walk Approximate a Random Permutation?, with Vishesh Jain, Tianren Liu, Angelos Pelecanos, Stefano Tessaro, and Vinod Vaikuntanathan. Submitted.
  5. The random graph process is globally synchronizing, with Vishesh Jain and Mehtaab Sawhney. Bulletin of the London Mathematical Society 58 (2026).
  6. Inducibility of rainbow graphs, with Emily Cairncross, Dhruv Mubayi. Mathematical Proceedings of the Cambridge Philosophical Society Volume 180, Issue 1, pp. 191--218 (2026).
  7. Rapid mixing of the down-up walk on matchings, with Vishesh Jain. APPROX/RANDOM 2024.
  8. Indeterminate cases of the Hamburger moment problem. Undergraduate senior thesis (2022).
  9. 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, Volume 55, Number 4 (2022).
  10. Generalizing Zeckendorf's theorem to homogeneous linear recurrences II, with Thomas Martinez, Steven J. Miller, Jack Murphy, Chenyang Sun. Fibonacci Quarterly 60:5, 231--254 (2022).
  11. Generalizing Zeckendorf's theorem to homogeneous linear recurrences I, with Thomas Martinez, Steven J. Miller, Chenyang Sun. Fibonacci Quarterly 60:5, 222--230 (2022).

Teaching

My office hours are listed on the MSLC website.

Outreach and Service