Research Overview

Our group explores problems in analysis and their applications in applied mathematics and mathematical physics. My main research areas include:

Asymptotic analysis

Investigates classical and modern asymptotic techniques, including differential equation methods (such as WKB approximations), difference equation methods, and integral approaches. Focuses on uniform asymptotics and their applications.

Orthogonal polynomials and special functions

Explores properties of orthogonal and multiple orthogonal polynomials for fixed degrees, as well as their large-degree asymptotics and applications. Investigates classical special functions, such as Airy, Bessel, and hypergeometric-type functions.

Integrable systems

Studies integrable ordinary differential equations, such as the Painlevé equations and their generalizations. Explores core integrable nonlinear PDEs such as the KdV, mKdV, nonlinear Schrödinger, and Boussinesq equations and their applications.

Random matrix theory

Examines spectral statistics for random unitary ensembles and determinantal point processes. Key topics include gap probabilities, partition functions, eigenvalue rigidity, and phase transitions near spectrum boundaries and singular points.

Riemann-Hilbert problems

Employs the Deift–Zhou nonlinear steepest descent method for Riemann–Hilbert problems as a unifying framework to investigate phenomena in random matrix theory and integrable systems.

Postdocs and PhDs

I have the privilege of working with the following researchers:

Ph.D. Students

  • Guangxiong Zhang (2026-current)
  • Chenhao Lu (2022-current)
  • Yu Zhai (2018-2022)
  • Luming Yao (2016-2021)
  • Weiying Hu (2014-2018)

Postdocs

  • Jia-Hao Du (2025-current)
  • Han-Han Sheng (2024-current)
  • Xiao-Lu Yue (2024-2026)