Research

Publications 

Arctic curves of periodic dimer models and generalized discriminants, Selecta Math. accepted,  arXiv:2410.17138

(slides)

Finer limit circle/limit point classification for Sturm–Liouville operators, with J. Stanfill, J. of Differential Equations, 471, 114372, 54 pp. (2026),

doi.org/10.1016/j.jde.2026.114372  (slides)

Wiener-Hopf factorizations and matrix-valued orthogonal polynomials related to the Aztec diamond,  with A. Kuijlaars, Probab. Math. Phys., 6(2), 547-580 (2025), doi.org/10.2140/pmp.2025.6.547 (slides)

The spectral ζ-function for quasi-regular Sturm–Liouville operators, with G. Fucci and J. Stanfill, Lett. Math. Phys., 115(8), 48 pages (2025), doi.org/10.1007/s11005-024-01893-x 

The Jacobi operator on (-1,1) and its various m-functions, with F. Gesztesy, L. Littlejohn and J. Stanfill, Complex Anal. Oper. Theory, 18(155), 69 pages (2024), doi.org/10.1007/s11785-024-01576-4 

Asymptotics of the Korteweg–de Vries shock waves via the Riemann–Hilbert approach, with I. Egorova and G. Teschl, Indiana Univ. Math. J., 73 No. 2, 645-690 (2024) (slides) 

Recurrence coefficients of polynomials with logarithmic weights, with P. Deift, SIGMA 20, 004, 48 pages (2024), doi.org/10.3842/SIGMA.2024.004  (slides)

Parametrix problem for the Korteweg–de Vries equation with steplike initial data, J. of Differential Equations, 375, 280–314 (2023), doi.org/10.1016/j.jde.2023.06.052

Donoghue m-Functions for Singular Sturm–Liouville Operators, with F. Gesztesy, L. Littlejohn, R. Nichols and J. Stanfill, St. Petersburg Math. J., 35(1), 134–183 (2023)

A scalar Riemann–Hilbert problem on the torus: Applications to the KdV equation, with G. Teschl, Anal. Math. Phys. 12(112), 1-19 (2022), doi.org/10.1007/s13324-022-00715-4 (slides)

The Jacobi Operator and its Donoghue m-Function, with F. Gesztesy and J. Stanfill, 28p., Conference Proceedings of IWOTA, Lancaster, UK 2021, Y. Choi, G.Blower and M. Daws (eds.), Operator Theory: Advances and Applications, Springer, Birkhäuser, doi.org/10.1007/978-3-031-38020-4 

Riemann-Hilbert Theory without local Parametrix Problems: Applications to Orthogonal Polynomials, J. Math. Anal. Appl. 125495 (2021), doi.org/10.1016/j.jmaa.2021.125495 (slides)

Preprints

Complex analytic theory of Sturm-Liouville operators with Schatten p-class resolvents, with G. Fucci and J. Stanfill, arxiv:2604.10115 

ζ-functions via contour integrals and universal sum rules, with G. Fucci and J. Stanfill, arXiv:2508.15699