- Geometric Methods in Hamiltonian Mechanics and Control Theory
- Celestial Mechanics
- Holonomic Quantum Computation

The common thread of most of my recent research is the geometry of fiber bundles and connections, as well as the consequences of symmetry in various hamiltonian systems. I have applied these ideas to topics as diverse as vortex dynamics and celestial mechanics. About the latter, of particular current interest is the symmetry associated to the N-body problem in non-euclidean spaces. An important aspect of the dynamics of Hamiltonian systems on fiber bundles with a principal connection is that of *holonomy*. I am interested in the use of holonomy for implementing quantum gates in quantum computers.

- Development for the Cardano Blockchain
- Haskell Programming Language
- Wolfram Language
- Computational Thinking in Math and Science Education
- Mathematics in Music Theory

Recent courses that I have taught at *Instituto Tecnológico Autónomo de México* (ITAM):

- Quantum Computation: physics and mathematics fundamentals
- Electromagnetic Theory
- Electromagnetic Radiation and Antennas
- Analytic and Vector Geometry

Future courses (ITAM, summer of 2021):

- Analytic and Vector Geometry
- Mathematics of Quantum Computation