Yuan Gao

Associate Professor of Mathematics

Department of Mathematics, Purdue University
Email：gao662@purdue.edu
Find me on Google Scholar or ResearchGate.
I mainly work on analysis/computations for PDEs from materials sciences, biology, and microfluids. I recently focus on optimal control and Hamilton-Jacobi equations with applications in transition path theory, mean-field limit, large deviation principle and non-equilibrium chemical reactions.
My research is supported by NSF Award DMS-2204288 and NSF CAREER Award DMS-2440651.
Delaware-Indiana-Maryland-Ohio-Pennsylvania Joint Seminar on Mathematical Data Science

Associate Professor of Mathematics, Department of Mathematics, Purdue University, 2026-Now
Assistant Professor of Mathematics, Department of Mathematics, Purdue University, 2021-2026
William W. Elliott Assistant Research Professor, Mathematics, Trinity College of Arts & Sciences, Duke University, 2019-2021

PDE analysis and multiscale modeling in materials sciences
- Crystal growth: high order degenerate parabolic equations, singularity characterization, hydrodynamic limit
- Dislocation: vectorial nonlocal Ginzburg-Landau systems, dynamic boundary condition, rigidity, metastability and slow motion
Numerical analysis and simulations for interface dynamics
- Obstacle problem: contact line dynamics, lubrication approximation, phase field model, nonlocal model, surfactant dynamics, linear response relation
Applied stochastic analysis and stochastic algorithm
- Reversible/irreversible Langevin dynamics: random walk on point clouds, transition path theory, optimal control, coarse-graining, ergodicity, large deviation, viscosity solution, Hamilton-Jacobi-Bellman equation, applications in image processing and sampling