Mark Williams
استاد · Partial differential equations
University of North Carolina at Chapel Hillمعرفی
Mark Williams is a Professor and Director of Undergraduate Studies in the Department of Mathematics at the University of North Carolina at Chapel Hill.
His educational background includes:
- B.S. in Mathematics from Knox College (1977)
- Ph.D. in Mathematics from MIT (1981)
Professor Williams' research focuses on partial differential equations, particularly in developing methods for obtaining qualitative information about solutions where explicit solutions are generally impossible. His work spans geometric optics, nonlinear elasticity, hyperbolic systems, and wave propagation phenomena. He has made significant contributions to understanding the behavior of solutions to complex differential equations through asymptotic analysis and mathematical physics approaches.
His publication record shows a consistent focus on geometric optics and wave propagation in various contexts, with particular attention to nonlinear phenomena, boundary value problems, and asymptotic methods. Over the past decade, his research has expanded to include more complex systems involving multiple amplification phenomena and high-order grazing of convex obstacles.
Professor Williams has collaborated extensively with researchers including J.-F. Coulombel, O. Gues, G. Metivier, and K. Zumbrun on numerous significant publications in top mathematics journals. His leadership role as Director of Undergraduate Studies demonstrates his commitment to mathematics education, as evidenced by his development of lecture notes covering advanced topics from multivariable calculus to functional analysis.
