Curriculum Vitae

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 Topology in Dynamical Systems: Conley Index Theory, Set Oriented Numerics, computational aspects of Morse/Floer theory, and Applications.
• A Posteriori Analysis and Numerics in Dynamical Systems: Parameterization of invariant manifolds with rigorous error bounds. Applications to computer assisted proof of connecting dynamics for diffeomorphisms, ordinary and 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-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)