Jian-Guo Liu

Jian-Guo Liu is a Professor of Physics and Mathematics at Duke University, affiliated with the Physics department and Trinity College of Arts & Sciences. He is also a Professor of Physics and Mathematics at Duke Kunshan University. His research interests include mathematical physics, computational methods, and data assimilation for complex systems. Liu has published extensively on topics such as the discrete Poincaré inequality, the Random Batch Method, and data assimilation models. He has received several grants from the National Science Foundation, including projects on dynamics, singularities, and nonlocal models. His work has been featured in journals such as the Quarterly of Applied Mathematics and the Mathematics of Computation.

Jian-Guo Liu is a professor in the Department of Mathematics and Department of Physics at Duke University. His research focuses on applied mathematics, particularly in partial differential equations, nonlinear dynamics, kinetic theory, and fluid mechanics. His work addresses complex systems such as flocking dynamics, chemotaxis-fluid models, and magnetohydrodynamics. Liu has contributed to the development of numerical methods for incompressible flows and explored the mathematical foundations of kinetic formulations. His research also includes the study of stochastic gradient descent and its diffusion approximations, as well as the analysis of vorticity boundary conditions and asymptotic-preserving methods.