Ph.D., University of Zürich, Switzerland (2013)
M.Sc.. University of Utrecht, the Netherlands (2009)
B.A., Universidad de los Andes, Colombia (2004)
My research lies at the intersection of geometry, topology and mathematical physics. There are two different ways to understand physical systems. One is called classical, the analysis of phenomena at a macroscopic level, and the other one is called quantum, which deals with the physics at the subatomic scale. My focus is on understanding and connecting these two different approaches by using tools of differential geometry like Lie groups, Lie algebras and Poisson structures. I am also interested in undergraduate research, in particular the applications of some of these techniques to network theory and information theory.
I enjoy teaching courses with a wide range of topics and levels, from Introductory Calculus and Linear Algebra to more advanced ones, such as Lie Groups and Lie Algebras, Differential Geometry and Graph Theory. I encourage active participation and discussions during the lectures, and I emphasize connections with other branches of science and knowledge. I have mentored several research projects with both undergraduate and high school students, on topics which involve pure mathematics and applications to physics and network theory.
You can see my personal website.