I joined IBM Research in 2016, working in Topological Data Analysis. By background is as follows:
I Graduated from the Escuela Superior de Fisica y Matematicas del Instituto Politecnico Nacional in Mexico in 2007, with a B.Sc. in Mathematics. My thesis was about normal closures of certain Kummer extensions.
I then obtained a Master's Degree in Mathematics at the Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional. My Master's thesis work was about stable cohomological operations, specifically about a topological proof of the Adem relations, a set of relations between generators of the Steenrod algebra.
My final degree, a Ph. D. in Mathematics was again at the Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional. My doctoral thesis consisted of giving bounds for the topological complexity -basically the number of simplest parts in some sense that you can decompose a space into- of real projective spaces. For this purpose, a big part of my thesis is about computations of cohomology rings of real projective spaces.
My graduate studies are, as visible here, focused on algebraic topology. In addition to the theoretical side, I have also always been curious about applications of algebraic topology to concrete problems; naturally topological data analysis is something to which I can contribute with my knowledge of theoretical constructs. In particular persistent homology is a tool which can be used to analyze information in computational biology.