Curriculum Vitae
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Contact Information
Associate Professor
Department of Mathematical Sciences
Florida Atlantic University
Science Building
Room 262
777 Glades Road, Boca Raton, Florida 33431
Telephone: (561)-297-3340
Email: jmirelesjames@fau.edu
Areas of Interest
- Computational Dynamics: Parameterization methods for invariant manifolds.
Globalization of local stable/unstable manifolds. BVP formulations for transverse intersections.
- A Posteriori Analysis for Functional Equations: computer assisted existence proofs for solutions
of nonlinear equatoins.
- Applications in nonlinear analysis: celestial mechanics, dynamics of delay differential
equations and parabolic partial differential equations.
- KAM Theory: existence and numerical approximation of invariant manifolds in spite of small divisors.
Education
- Ph.D. Mathematics. University of Texas at Austin. December 2009.
Thesis Advisor: Rafael de la Llave.
- B.S. Mathematics Lamar University, Beaumont, Texas, 2003.
- B.S. Electrical Engineering, Lamar University, Beaumont, Texas, 2003
Ph.D. Dissertation
- "Reliable Computation of Invariant Dynamics for Conservative Discrete Dynamical Systems"
Research Support
-
National Science Foundation Grant DMS - 2307987:
``Fine Structure in Hamiltonian Systems'' (July 2023 - June 2026).
-
National Science Foundation Grant DMS-1813501: ``Validated
Computational Methods in Global Analysis and Applications to
Celestial Mechanics'' (August 2018-July 2021).
- National Science Foundation Grant DSM - 1318172: ``Computational Intersection
Theory for Infinite Dimensional Dynamical Systems'' (July 2013 - August 2016)
- AMS Simmons Travel Grant. (Awarded in Summer 2013)