I have spent most of my academic career at universities in the United States, with a more recent chapter in Chile and sabbatical visits to Switzerland and the UK.

My research lies at the interface of applied mathematics, stochastic analysis, and computational biology. Broadly speaking, I am interested in how randomness, geometry, and biophysical mechanisms combine to shape the behavior of complex systems.

In recent years, my research has also expanded into data-driven modeling and machine learning, with particular emphasis on high-performance computing, Bayesian inference, and molecular dynamics.

Some of my current and past work includes:

• Stochastic optimization and machine learning, including the dynamics of stochastic gradient descent on manifolds and connections to biological search processes; see, for example, our work on stochastic gradient descent with autocorrelated noise.
• Bayesian learning and uncertainty quantification; see, for example, our work on molecular dynamics, epidemics in population networks, detection of arterial wall abnormalities, and DNA methylation.
• Mesoscale computational modeling, including dissipative particle dynamics and related approaches; see, for example, our work on lipid bilayer membranes, DNA diffusion in nanofluidic devices, and biological microswimmers.
• Multiscale modeling, particularly effective descriptions of transport in complex biological geometries; see, for example, our work on oxygen transport in arterial networks and reconstructive tissue flaps.

I also enjoy working on problems with a more theoretical flavor, particularly those involving stochastic partial differential equations, random media, and stochastic homogenization.

Over the years, I have been fortunate to receive external research funding in both the United States and Chile, including two grants from the US National Science Foundation. My NSF CAREER award supported, among other projects, my work on Bayesian model selection for molecular dynamics. More recently, my research in Chile was supported by a Fondecyt Regular grant.

I currently serve as an Associate Editor for the mathematics section of Royal Society Open Science.