Additional Participants

Graduate Student

Jan Fiala
Jacob Simmons

Undergraduate Student

Vitaly Tkachuk

Organizational Partners

Max Planck Institute for Mathematics
College de France
University of Nottingham
Queen Mary, University of London
University of Michigan Ann Arbor
Cardiff University

Project Period


Level of Access

Open-Access Report

Grant Number


Submission Date



This research focuses on the exact study of the statistical mechanics of model systems. Research concentrates on critical percolation in two-dimensions, and important and extensively studied statistical system, and the phase transition of the farey fraction spin chain, a new and interesting one-dimensional model with connections to multifractals and Monte Carol simulations, mathematically exact solutions of model statistical mechanical systems, and techniques from number theory. The goal is to gain new insights into, and understanding of, these systems. An important feature of the project is the use of techniques from pure mathematics and close collaboration with mathematicians.