Analysis & Differential Equations
The Analysis & Differential Equations cluster is dedicated to the rigorous study of differential equations and dynamical systems, including nonlinear and stochastic PDEs, integrable systems, and their applications in modeling physical and biological phenomena. Our work includes the development of both analytical and computational techniques for solving these equations.
Faculty in this cluster investigate fundamental questions, such as how diffusion alters the stability and global dynamics of steady states in reaction-diffusion equations. We also design and analyze novel numerical methods for complex systems, including the simulation of compressible flows which may contain shocks or other discontinuities. This research provides the foundational analysis that supports many of the applied and computational areas within the department.
Affiliated Faculty
Our faculty are leaders in the theoretical and computational analysis of complex systems. Explore their profiles to learn more.
Tommaso Buvoli (Primary)
Professor Buvoli's research focuses on creating, analyzing, and applying novel numerical methods to solve challenging differential equations that arise in multiscale dynamical systems. View Profile »
Ricardo Cortez (Secondary)
Professor Cortez develops and analyzes computational methods for simulating biological fluid flows, providing a crucial link between fundamental mathematics and applied biomedical science. View Profile »
Maurice Joseph Dupre (Primary)
Professor Dupre's research applies methods from topology and geometry to problems in functional analysis, with connections to mathematical physics and general relativity. View Profile »
Lisa J. Fauci (Secondary)
Professor Fauci uses computational methods, modeling, and simulation to investigate biological systems where flexible structures interact with a fluid. View Profile »
Kenneth McLaughlin (Primary)
A distinguished chair, Professor McLaughlin's research is in integrable systems, using asymptotic analysis of Riemann-Hilbert problems with applications to random matrix theory and nonlinear wave equations. View Profile »
Victor Moll (Secondary)
Professor Moll is a classical analyst with deep interests in the evaluation of definite integrals, special functions, and number theory, often employing symbolic computation. View Profile »
Samuel Punshon-Smith (Primary)
Professor Punshon-Smith's research focuses on the analysis of PDEs arising in fluid mechanics, using stochastic analysis and random dynamical systems to understand chaos and turbulence. View Profile »
Norbert Riedel (Primary)
Professor Riedel's work is in functional analysis and mathematical physics, including contributions to operator algebras and the theoretical foundations of statistical learning. View Profile »
Frank Tipler (Primary)
A mathematical physicist, Professor Tipler's research involves global general relativity, quantum field theory, and quantum cosmology. View Profile »
Kun Zhao (Primary)
Professor Zhao's research centers on the qualitative and quantitative properties of nonlinear PDE models arising from mathematical biology and fluid dynamics. View Profile »
Seminars & Activities
- Faculty and students in this cluster are active participants in the department's weekly Integrability and Beyond! Seminars.
- Explore all faculty profiles in the Mathematics Department Directory.
