Ahmad Barhoumi

Department of Mathematics, Grinnell College

Office: Noyce 2611 Email: barhoumia@grinnell.edu Tel.: (641)269-4927

Research Interests

I am an analyst thinking about problems coming from approximation theory, integrable systems, and special function theory. Recently, I have become interested in random tiling models and, more broadly, the area of integrable probability.

List of Publications

  1. [Arxiv] Universal Asymptotics and Exact Enumeration of Eulerian Maps.
    - with R. Gharakhloo and N. Hayford. Under Review, 65 pages.
  2. [Arxiv] The \(q^\text{vol}\) lozenge tiling model via non-Hermitian orthogonal polynomials.
    - with M. Duits. Under Review, 50 pages.
  3. [Arxiv, DOI] Asymptotics of polynomials orthogonal with respect to a generalized Freud weight with application to special function solutions of Painlevé-IV.
    - Stud. Appl. Math. (2024) 153, no. 3, Paper No. e12738, 48 pages.
  4. [Arxiv, DOI] On Airy solutions of PII and complex cubic ensemble of random matrices, II.
    - with P. Bleher, A. Deaño, and M. Yattselev. In: Contemp. Math. 822 (2025), 26 pages.
  5. [Arxiv] Painlevé-III Monodromy Maps Under the \(D_6 \to D_8\) Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions.
    - with O. Lisovyy, P. Miller, and A. Prokhorov. SIGMA 20 (2024), 019, 77 pages.
  6. [Arxiv, DOI] On Airy solutions of PII and complex cubic ensemble of random matrices, I.
    - with P. Bleher, A. Deaño, and M. Yattselev. In: Proceedings of the 16th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA-16), 205–220. CRM Ser. Math. Phys. (2025), 12 pages.
  7. [Arxiv, DOI] Non-Hermitian Orthogonal Polynomials on a Trefoil.
    - with M. Yattselev. Constr Approx (2023) 59, 61 pages.
  8. [Arxiv, DOI] Investigation of the two-cut phase region in the complex cubic ensemble of random matrices.
    - with P. Bleher, A. Deaño, and M. Yattselev. J. Math. Phys. 63 (2022), 063303, 40 pages.
  9. [Arxiv, DOI] Strong asymptotics of Jacobi-type kissing polynomials.
    - Integral Transforms Spec. Funct. 32 (2021), 5-8, 18 pages.
  10. [Arxiv, DOI] Global-phase portrait and large-degree asymptotics for the Kissing polynomials.
    - with A. F. Celsus, and A. Deaño. Stud Appl Math. 147 (2021), 79 pages.
  11. [Arxiv, DOI] Asymptotics of polynomials orthogonal on a cross with a Jacobi-type weight.
    - with M. Yattselev. Complex Anal. Oper. Theory 14 (2020), 44 pages

Editorial work

  1. [DOI] Recent Developments in Orthogonal Polynomials
    - Co-edited with R. Gharakhloo and A. Martinez-Finkelshtein. Contemp. Math. 822 (2025)

“The best thing for being sad," replied Merlin, beginning to puff and blow, "is to learn something. That's the only thing that never fails. You may grow old and trembling in your anatomies, you may lie awake at night listening to the disorder of your veins, you may miss your only love, you may see the world about you devastated by evil lunatics, or know your honour trampled in the sewers of baser minds. There is only one thing for it then — to learn. Learn why the world wags and what wags it. That is the only thing which the mind can never exhaust, never alienate, never be tortured by, never fear or distrust, and never dream of regretting. Learning is the only thing for you. Look what a lot of things there are to learn.”

― T.H. White, The Once and Future King