Yen Do

Yen Do is an Associate Professor in the Department of Mathematics at the University of Virginia. His research lies at the intersection of Analysis, Probability, and Partial Differential Equations, with a focus on problems involving random polynomials, time-frequency analysis, and nonlinear integrable equations.

Research Interests include:

• Time-Frequency Analysis: Multilinear estimates for operators with modulation invariance, inspired by Carleson's work on Fourier series convergence.
• Random Polynomials and Functions: Studies on the distribution of real roots, expectation, variance, asymptotic normality, and law of large numbers for root counts.
• Nonlinear Integrable Equations: Long-time asymptotics for solutions of nonlinear PDEs, extending oscillatory integral techniques to nonlinear settings.

Publications reflect a consistent exploration of harmonic analysis, probabilistic root distribution, and operator theory. His work spans topics like random orthogonal polynomials, Carleson embeddings, and variations in bilinear operators, often addressing fundamental questions in probability and analysis.

Advising and Grants: Yen Do has advised

• Nhan Nguyen (2019-2023)
• Mark Lewers (2017-2020)

His research is supported by multiple NSF grants (DMS-1800855, DMS-1521293, DMS-1201456).