About

I am an Assistant Professor at the Institute for Mathematical and Computational Engineering (IMC) of the Pontificia Universidad Católica de Chile in Santiago.

From 2018 to 2021 I held an H.C. Wang Assistant Professorship at the Department of Mathematics of Cornell University. Before that, I received a Ph.D. in computational and applied mathematics from the Oden Institute (formerly ICES) of The University of Texas at Austin, where I was supervised by Professor Leszek Demkowicz. In 2017, I was a Geophysical Fluid Dynamics fellow at the Woods Hole Oceanographic Institution (WHOI). Previously, I obtained a M.Sc. in computational methods in aeronautical engineering from Imperial College London, and bachelor’s degrees in both mathematics and mechanical engineering from the Universidad de los Andes (Colombia).

My research lies in the interdisciplinary intersection of mathematics, physics, engineering and computational science. More specifically, I do research in computational mathematics that involves numerical analysis and nonlinear dynamics. Within numerical analysis, I am interested in finite element methods and applied functional analysis. In the last few years, I have helped develop some of the latest advances in discontinuous Petrov-Galerkin (DPG) methods, which are very effective at solving partial differential equations (PDEs), and have many physical applications. Within nonlinear dynamics, I like to study hydrodynamic stability of classical flows, like plane Couette flow. Here, (fluid) dynamical systems are posed in the form of a semidefinite program (SDP) with sum-of-squares (SOS) constraints, and then a computer is used to derive some important stability properties of the dynamical system. Recently I’ve been trying to combine these two lines of research. Learn more details about my research here.

When I’m not doing research I’m probably either playing or watching “fútbol”. My clock definitely stops ticking every four years for the World Cup. In my free time I also love to watch movies and TV series (advanced user: several thousand hours under my belt), browse youtube, read the news, enjoy books, and watch other sporting events like tennis (all hail Roger Federer) and baseball (go Cards!).