Last Updated 05/Jul/2017
I am currently a Prager Assistant Professor at Brown University. I received my bachelor's degree in mathematics from Los Andes University in Bogotá, Colombia, in 2010. I finished my Ph.D in mathematics at Carnegie Mellon University in 2015; my adviser was Dejan Slepčev.
My research lies at the intersection of calculus of variations, geometric measure theory, optimal transportation and the applications of these areas to problems that arise from data analysis, machine learning and statistics. In particular, my research focuses on the study of the convergence of solutions of minimization problems in random geometric graphs, to solutions of analogous minimization problems in the continuum. The minimization problems of interest are those connected to important tasks in machine learning like clustering, dimensionality reduction, and classification.
More recently I have been also interested in Bayesian inverse problems related to PDEs and modeling in physics, mathematical finance and data analysis.