Research Interests

My research in probability theory concerns problems that arise from ecology and genetics. In the case of ecology, this means the study of stochastic spatial models and how their properties differ from the homogeneously mixing situation, which is usually modeled by differential equations. Much of this work has been done in collaboration with Simon Levin at Princeton. In genetics, I have developed mathematical models to study the evolution of microsatellites, impacts of selective sweeps on genetic variation, genome rearrangement, gene duplication and gene regulation. The last topic, which can be thought of abstractly as waiting for some individual to accumulate k prespecified mutations, leads naturally to the study of multistage carcinogenesis and has interested me in the analysis of data generated by cancer genome projects.

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Section 32: Applied Mathematical Sciences