Dynamics
The 3-Body Problem
The 3-body problem is one of the oldest questions in mathematical physics. It can be posed quite simply: given three point particles interacting under the effect of their mutual Newtonian gravitational fields, what is the long-term evolution of the system? Analytic perturbation theory can be used to find closed-form solutions when hierarchies (in either mass or separation) exist, but the non-hierarchical 3-body problem is famously resistant to analytic solution due to its intrinsically chaotic nature. Recently, my work with Nathan Leigh has demonstrated that a closed-form statistical solution exists to the chaotic 3-body problem, one which can be found via the ergodic hypothesis. My group is investigating a number of extensions and applications of this new statistical solution.
Collisional Runaways
The prototypical laboratories for astrophysical dynamics are the dense star clusters which inhabit galaxies like the Milky Way. When these clusters were young, near the beginning of the Universe, their dense central regions may have hosted runaway collisions: repeated mergers of stars with one another that built up a very massive star, which upon its death could form an intermediate-mass black hole (IMBH). A loosely analogous process of IMBH formation may occur today, in the densest nuclear star clusters, although in this case the IMBH would be formed from stellar-mass black hole seeds.