I am a probabilist and statistician working in the general area of stochastic processes and their applications. In the past, I have collaborated with Persi Diaconis and others on random matrices and various other aspects of probability on algebraic structures. I have numerous publications with Martin Barlow, Ed Perkins, Klaus Fleischmann, Tom Kurtz, Xiaowen Zhou, and Peter Donnelly on Dawson-Watanabe superprocesses and other measure-valued processes that arise in population biology, as well as with Jim Pitman on various coalescent models that appear in biology, chemistry and astrophysics. In the past, I have worked with Terry Speed, Mary Sara McPeek, Xiaowen Zhou, and others on phylogenetic invariants and interference regarding recombination.
I share an ongoing interest in biodemography with David Steinsaltz and Ken Wachter that has resulted in papers on fitness landscapes, mutation-selection balance, stochastic PDE models of bacteria and yeast aging, and applications of quasistationarity to mortality modeling.
I continue research on probability and real trees, particularly applications of ideas from metric geometry such as the Gromov-Hausdorff metric, some of it in collaboration with Tye Lidman, Jim Pitman, and Anita Winter. I am investigating tree statistics and most recent common ancestors in diploid populations with Erick Matsen. Monty Slatkin and I are researching allele frequency spectra for time-varying population sizes.
I am in the middle of an extensive project involving Tandy Warnow, Don Ringe, Luay Nakhleh, and Francois Barbancon on several aspects of phylogenetic inference - particularly applications of computational phylogenetic methods in historical linguistics.
I currently have students working on stepping stone models and coalescent sticky flows, the population genetics of hybrid zones, random matrices associated with Coxeter groups, random matrices arising from random trees and random networks, infinite-dimensional dynamical systems applied to mutation-selection balance, and connections between matrix-valued orthogonal polynomials and queuing theory.