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Department of Mathematical Sciences
Florida Atlantic University
777 Glades Road, Boca Raton, Florida 33431
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.
- 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
- "Reliable Computation of Invariant Dynamics for Conservative Discrete Dynamical Systems"
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)