My research interests are in equilibrium statistical mechanics in general, and more particularly in discrete models of phase transitions. As these are often equivalent to a combinatorial problem, I am equally interested in the relevant combinatorics, and the connection between the two. Additionally, I am regularly looking for new ways to count the underlying graphs efficiently. This leads me into a study of algorithmic complexity.
Current Research Projects
Stieltjes moment sequences: identifying combinatorial sequences as moments.
New scaling laws for self-avoiding walks
Identifying the theta-point of interacting self-avoiding walks
Implementing smarter algorithms to count graphs in a variety of statistical mechanics models
Trying to prove the existence of a critical exponent for self-avoiding walks in two- and three-dimensions.
Numerical studies of certain groups, such as Thompson’s groups.
Occasional problems in number theory.