NICOLÁS GARCÍA TRILLOS
I am currently an Assistant Professor in the Department of Statistics at the University of Wisconsin Madison. From 2015 - 2018, I was a Prager Assistant Professor (postdoctoral position) at Brown University. I finished my Ph.D in mathematics at Carnegie Mellon University in 2015; my adviser was Dejan Slepčev. I received my Bachelor's degree in mathematics from Universidad de Los Andes in Bogotá, Colombia, in 2010.
Broadly speaking, my main academic interests lie in the fields of applied analysis, computational probability and statistics, and machine learning; my academic background is a mixture of mathematical analysis and statistics.
One of my main lines of research lies at the intersection of calculus of variations, optimal transport, and PDEs, and studies the connections between graph-based techniques for learning and continuum problems modelled by PDEs and calculus of variations. In my work I have developed mathematical tools to study large sample asymptotics for such graph based problems and have studied some of the computational implications of this analysis. From a purely mathematical point of view this line of work can be seen as studying the continuum limits of analytical structures defined on random geometric graphs.
Another of my lines of research involves the use of Bayesian methods for inference and MCMC computing in the context of uncertainty quantification for inverse problems arising in physics and engineering. In such problems the main computational challenge is the cost of evaluating an expensive forward map. This challenge is fundamental to the Bayesian inversion of complex models since vanilla MCMC sampling methods require repeated evaluation of the forward map. I have been working on developing a general data-driven framework for efficient discretization of forward maps, where for example the spatial refinement of a grid is informed by observed data.