Nathan Hayford

Hi!

I am a postdoctoral Assistant Professor at the University of Michigan (UM) working with Peter Miller and Jinho Baik. Before that, I was a postdoc in the department of mathematics at the Royal Institute of Technology (KTH) working with Maurice Duits, and before that I did my graduate studies at the University of South Florida (USF) with Razvan Teodorescu and Seung-Yeop Lee.

If you have any questions, feel free to send me an email at:

nhayford [at] umich.edu

Research Interests

I work mostly on problems in complex analysis and mathematical physics.

A few of my interests are:

Random matrix theory
Conformal field theory and 2D quantum gravity
Statistical mechanics and exactly solvable lattice models
Integrable combinatorics
Riemann-Hilbert problems and orthogonal polynomials
Free boundary problems

List of Publications

A. Barhoumi, R. Gharakhloo, & N. Hayford, Universal Asymptotics and Exact Enumeration of Eulerian Maps. arXiv preprint, 2026.
M. Duits, N. Hayford, & S.-Y. Lee, The Ising Model Coupled to 2D Gravity: Critical Partition Function. arXiv preprint, 2026.
M. Alameddine, N. Hayford, & O. Marchal, The Painlevé I hierarchy: Correspondence between the isomonodromic approach and the minimal models of the KP hierarchy. Ann. Henri Poincaré (2026).
N. Hayford, Asymptotic Properties of a Special Solution to the (3,4) String Equation. J. Phys. A: Math. Theor. 58 (43), 2025.
N. Hayford, The Ising Model Coupled to 2D Gravity: Higher-order Painlevé Equations/The (3,4) String Equation . arXiv preprint, 2024.
M. Duits, N. Hayford, & S.-Y. Lee, The Ising Model Coupled to 2D Gravity: Genus Zero Partition Function. SIGMA 21 (79), 2025.
N. Hayford & F. Wang, A Note on Electrified Droplets. Comput. Methods Funct. Theory 54, 2021.
A. Abanov, N. Hayford, D. Khavinson, & R. Teodorescu, Around a theorem of F. Dyson and A. Lenard: Energy Equilibria for Point Charge Distributions in Classical Electrostatics. Expositiones Mathematicae 39 (2), 2021.

Upcoming Events

These are events I am planning on attending, pending unforeseen circumstances.

Integrable Systems, Waves and Asymptotics, May 24th-28th, Bristol, UK
AMS Spring Central Sectional Meeting, April 17th-19th, Iowa City, IA
AMS Fall Western Sectional Meeting, November 7th-8th, Tempe, AZ
SIAM TX-LA Annual Meeting, October 30th-November 1st, Dallas, TX

Recent/Upcoming Talks

(November 2026) AMS Fall Western Sectional Meeting
(October 2026) SIAM TX-LA Annual Meeting
(September 2026) UM Probability and Analysis Seminar
(July 2026) SIAM Annual Meeting
(November 2025) Journée cartes à Jussieu
(May 2025) Nordita High Energy Physics Seminar

Me talking at Great Bay University in June 2024.

Translational Work (Not much, but I gave it an attempt)
I recently translated a paper by A. A. Kapaev ("Asymptotic behavior of the solutions of the Painlevé equation of the first kind", Differ. Uravn. 24 (10), 1986, p. 1684-1695), and am sharing it here for anyone who wants it.

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