In general, I work in theoretical evolutionary ecology. In particular, I'm investigating the sources and consequences of spatial heterogeneity.
Even though my training is in pure mathematics, I was a postdoctoral research associate in the Webb lab and with PRIMES, the program for
interdisciplinary mathematics, ecology and statistics. This article in
Nature says a tiny bit about how I came to be there.
Simulations
My work makes approximately equal use of pure mathematics and computer
simulations, all informed by ecology. You can get a very good idea of
what I'm doing by looking at these
simulations yourself. Caveat: If your web browser isn't
Java-enabled, this won't be much fun.
How does selection mediated by a spatially spreading disturbance affect individual-level dispersal and population-level spatial structure? We investigate this question with a birth-death process on a lattice on which a spatially spreading disturbanvce is imposed. We consider three different scenarios affecting whether an individual recovers from disturbance, corresponding to different trade-offs between short- and long-distance dispersal. In addition to computer simulation, we use a pair approximation to conduct an invasion analysis of different dispersal strategies. Of the trade-offs we examined, only a context-sensitive recovery, in which an individual's survival probability is enhanced by the presence of weaker neighbors, results in a mixed dispersal strategy. (With Colleen Webb. Evolutionary Ecology Research, 8(8), December 2006, 1377-1392.)
We consider a spatially-explicit birth death process in which organisms can reproduce using local dispersal, long-distance dispersal, or a mixed strategy. We approximate the system with a pair of equations which, empirically, does an excellent job of capturing the dynamics of the system. We use this approximation to view spatial aggregation through the lens of percolation theory. In doing so, we correct a pervasive mistake in the literature. (With Colleen Webb. Theoretical Population Biology, 69(2), March 2006, 155-164.)
This isn't, strictly speaking, a paper about biology; but my interest in complex networks is grounded in biology.
For a given natural number N, Corso constructs a graph with vertices {2,...,N}. He analyzes this family of graphs with computer calculations; I get exact answers using number theory. (Physical Review E, 70(5), 2004.)