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

Pattern-avoiding permutations.

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.