research
Broadly speaking, I am interested in asymptotic analysis, approximation theory, special function theory, and their application to problems in mathematical physics and random matrix theory. One of the main tools I use is the Riemann-Hilbert problem; for a nice introduction to the method as it applies to integrable systems, see Alexander Its' Notices article.
Below you will find some of my published papers as well as some preprints. If you have trouble accessing any of these publications, please let me know and I'll be happy to share a preprint! Many (but not necessarily all) of my preprints are also available on the arxiv.
Publications
A. B. Barhoumi and M. L. Yattselev. Non-Hermitian Orthogonal Polynomials on a Trefoil. Constr Approx (2023). https://doi.org/10.1007/s00365-023-09640-6 [PDF].
A. Barhoumi, P. Bleher, A. Deaño, and M. Yattselev. Investigation of the two-cut phase region in the complex cubic ensemble of random matrices. J. Math. Phys. (2022); 63, 063303 https://doi.org/10.1063/5.0086911
A. B. Barhoumi. Strong asymptotics of Jacobi-type kissing polynomials. Integral Transforms Spec. Funct. (2021); 32:5-8, 377-394, doi: 10.1080/10652469.2021.1923707
A. Barhoumi, A. F. Celsus, and A. Deaño. Global-phase portrait and large-degree asymptotics for the Kissing polynomials. Stud Appl Math. (2021); 147: 448– 526. https://doi.org/10.1111/sapm.12387
A. Barhoumi and M. L. Yattselev. Asymptotics of polynomials orthogonal on a cross with a Jacobi-type weight. Complex Anal. Oper. Theory (2020); 14, 9 doi:10.1007/s11785-019-00962-7
Work Submitted or in Preparation
A. Barhoumi, P. Bleher, A. Deaño, and M. Yattselev. On Airy solutions of PII and complex cubic ensemble of random matrices, I. Submitted [PDF].
A. Barhoumi, O. Lisovyy, P. Miller, and A. Prokhorov. Large-degree rational solutions of the Painlevé III equation near its fixed singular point. In preparation.
A. Barhoumi, P. Bleher, R. Gharakhloo, and K. T-R. McLaughlin. Topological Expansion in the Complex Quartic Random Matrix Model: Two-cut Case. In preparation.
Dissertation
A. Barhoumi. Orthogonal Polynomials on S-Curves Associated with Genus One Surfaces. Diss. 2020. http://hdl.handle.net/1805/23029