At a high level, I am interested in devising fast algorithms with provable guarantees for various problems in (combinatorial and continous) optimization, machine learning and database theory (though I am easily excited by any theoretical problem!). I've also been excited about problems in random matrix theory and stochastic processes. In general, there seems to be some amazing connections between continous methods for dealing with combinatorial problems in optimization and high-dimensional probability which I'm very excited to explore!