Yan Guo Professor of Applied Mathematics, Chair of Applied Mathematics

Professor Guo received his B.S. from Peking University in 1987. He received his Ph.D in Mathematics from Brown University in 1993. He was a Courant Instructor at the Courant Institute of Mathematical Sciences for 1993-95. He joined the faculty of the Division of Applied Mathematics at Brown University as an Assistant Professor in September 1995. He was an Assistant Professor at Princeton University for 1996-97. His professional awards include an Honorable Mention in SIAM Student Paper Competition in 1992, an A. P. Sloan Dissertation Fellowship in 1993, an NSF Postdoctoral Fellowship for 1995-98. Professor Guo is an A. P. Sloan Research Fellow for 1998-2000. He was named a Manning Assistant Professor at Brown for 1998 to 1999, and was promoted to an Associate Professor in 1999 and then Professor in 2004. He is a Simon Research Fellow from 2015 to 2016.

Brown Affiliations

Research Areas

research overview

Professor Guo's research is concerned with the rigorous mathematical study of partial differential equations arising in various scientific applications, such as kinetic and fluid models for plasma physics, vortices in classical field theory (superconductivity and superfluidity), and stability problems in stellar dynamics, and other physical problems.

research statement

Professor Guo's research is concerned with the rigorous mathematical study of partial differential equations arising in various scientific applications. More specifically, he has been working on PDE arising in
the kinetic theory of statistical physics, especially in connection with the nonlinear stability of their steady states. Kinetic theory is concerned with the study of the dynamics of a large ensemble of 'particles'. Interestingly, such abstract 'particles' can be tiny
gas molecules, or enormous stars in a galaxy. The most fundamental equation in the kinetic theory for describing gas molecules is the celebrated Boltzmann equation. Many fundamental macroscopic fluid
equations, such as the Euler and Navier-Stokes equations, can be derived from the Boltzmann theory. He has been working on stability of Maxwellian states in the Boltzmann theory. In a kinetic theory of stars, collisions among stars are sufficiently rare to be ignored. Therefore, a galaxy or a globular cluster can be modeled as an
ensemble of particles, i.e., stars, which interact only by the gravitational field which they create collectively. The time evolution of a galaxy can then be described by the Vlasov theory. There are many well known steady state galaxy models. Professor Guo has been developing mathematical tools to analyze the dynamical stability of these steady galaxy models. Instabilities of equilibria in many physical and biological sciences has always attracted great attention. It is important, from a scientific point of view, to understand the rate, time scale, structure, pattern and dynamics of various instabilities in a fully nonlinear setting. Professor Guo has been working on developing general mathematical framework to prove and characterize such nonlinear instabilities.

funded research


 `PDE methods in kinetic theory and their applications.'