Research Opportunities for Students

• nonlinear models--Besides gravity, there are a number of mathematical models which are quite interesting and which require computational modeling to really understand them. These models are a bit simpler than gravity, and yet their phenomena are not well understood. Examples include Q-Balls, Skyrmions, the Faddeev-Skyrme model for Hopf solitons, monopoles, domain walls, and strings. There are also mathematical questions (e.g. of global existence) with a variety of geometrically motivated models and with the nonlinear Schroedinger Equation.
   
• emergent phenomena--I'm also interested in various other phenomena, in particular emergence, agent based modeling, traffic modeling (see the draft of a book by a leader in the field), and computational finance.
   
• distributed computing--supercomputers these days generally consist of large numbers of individual "computers" networked together. To be able to treat them as a single machine for computing purposes, one needs to be able to write software that "talks" to its constituent pieces. I do this with something called message passing interface (MPI) and also OpenMP, and there are lots of projects investigating how best to use MPI and OpenMP.
   
• black hole excision--Writing a code which will evolve black holes is a large project, but I've already got one. One thing I need though is for someone to extend the code to cut out the center of the black hole, the singularity, which causes all sorts of computational problems. Finding the horizons of black holes is another needed tool which presents some interesting computational challenges.