I design and analyze optimization and Markov Chain Monte Carlo sampling algorithms, with provable runtime, robustness, and privacy guarantees for applications in Machine Learning,  Data Science, and Statistics.  In doing so, I aim to introduce new mathematical tools from physics and geometry to the design and analysis of optimization and sampling algorithms used in ML. 

I am especially interested in Markov chain and stochastic gradient-based optimization and sampling algorithms.  These algorithms are used to rapidly explore a high-dimensional or non-convex function or probability distribution in applications such as deep learning and Bayesian statistics.  I am also very interested in the application of these algorithms to problems in machine learning, differential privacy, data science, theoretical computer science, and statistics.