J.D. Mireles James
Hill Assistant Professor
Hill Center for the Mathematical Sciences
Starting in the fall of 2014 I will be in the Department of Mathematics at Florida Atlantic University.Research interests include:
- The computer as the mathematician's "laboratory" for studying global dynamics of nonlinear systems. I'm especially interested in the computation and visualization of smooth invariant manifolds.
- Reformulation of qualitative questions about nonlinear dynamical systems into quantitative functional equations, and the subsequent study of those equations. The Parameterization Method for invariant manifolds is one of many outstanding examples of this paradigm.
- Rigorous numerical methods and computer assisted proof in analysis, especially constructive a-posteriori existence (or "shadowing") theorems for invariant manifolds, connecting dynamics, and chaotic motions.
Ph.D. Thesis: Reliable Computation of Invariant Dynamics in Area and Volume Preserving Discrete Dynamical Systems.
Ph.D. Advisor: Rafael de la Llave.
Postdoctoral Supervisor: Konstantin Mischaikow.