Research

I am broadly interested in applied probability with applications in mathematical biology, population genetics, and stochastic networks. Below I describe a few of my main research areas and projects within those areas:

Rare events in Markov processes
Stochastic processes in cancer biology
Mathematical models of cancer stem cells

Rare events in Markov processes

One main area of interest is rare event analysis and the design of optimal simulation techniques for estimating rare event probabilities. Rare event estimation problems arise in many applications, including stochastic queueing networks (arising in communication and manufacturing models), risk and reliability analysis, and also problems in evolutionary biology and ecology. Large deviations theory is a method of characterizing the asymptotic likelihood of a rare event and also the asymptotically most likely method for a rare event to occur. I have been interested in large deviations analysis of Markov processes and establishing importance sampling algorithms via game-theoretic approaches.





Stochastic processes in cancer biology

Many interesting mathematical problems arise from the study of evolutionary processes and population genetics. I have been particularly interested in applying mathematical models to study the evolutionary processes at the cellular level which occur during the initiation, progression, and treatment of cancer.