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Research interests

My research lies in random polynomial theory, at the intersection of probability, stochastic processes, analysis, and combinatorics. Random polynomials arise naturally in models involving randomness or noise, including differential and difference equations with random coefficients, partial differential equations with random initial data, and the spectral theory of random matrices. They also appear in applications ranging from numerical analysis and statistical regression to quantum chaos, communication systems, and mathematical physics.

A central theme of my work is the study of random roots, particularly the distribution and number of real zeros, which form intricate random point processes. I investigate their variance, limiting distributions, and concentration phenomena across a range of polynomial ensembles.

Earlier in my career, I worked on real analysis, integral transforms, operational calculus, functional analysis, ordinary and partial differential equations, and operator theory.

Recent updates

• May 26, 2026: Yen Q. Do, Nhan D. V. Nguyen, and Sean O'Rourke, Real roots of non-centered random polynomials, 75 pages, 2026, submitted. [arXiv:2605.26402]

• May 11, 2026: Summer REU, Critical Points of Random Polynomials [Link]

Co-mentor: Sean O'Rourke

Date: May 11 - June 26, 2026. 

Graduates: Hongkai Zhu, Eskil Irgens, and Shashi Balla

Undergraduates: Sarah Asres, Maxwell Allington, Anson Haffey, and Jacob Horwitz