I want to develop mathematics and computational methods to better understand and manipulate biochemical systems. It turns out that stochastic processes, and specifically continuous-time Markov chains, are good models for biochemistry under certain conditions. Since such models are typically very complex, simulating their time series is computationally demanding, so I use mathematics to develop more efficient numerical methods for such simulations.
The goal is to develop efficient algorithms to make analysis of large-scale models more tractable. I am also very interested in optimization algorithms, and how they can be applied to stochastic models in order to inform real biochemical manipulations. As part of the optimization research, I would like to develop better numerical methods for estimating parameter sensitivities of stochastic processes.