Research Interests (John Palmer)

I am interested in the mathematics that is being developed to understand certain exactly solvable models in Statistical Mechanics and Quantum Field Theory. These models include the scaling limits of the two dimensional Ising model and more generally a class of two dimensional Quantum Fields known as Holonomic Fields (they are called holonomic because of the intimate connection that they have with holonomic, or maximally overdetermined, systems of differential equations). The correlation functions for these models can be studied in some detail because there are Fredholm determinant formulas for them and in addition they can be characterized as tau functions for monodromy preserving deformations. These tau functions are best understood as determinants of Dirac operators with branch type singularities in their domain and from this point of view the theory has connections with much recent work on the index theory for Elliptic operators.

John Palmer / Department of Mathematics / Program In Applied Mathematics / University of Arizona / last revised Dec 10, 1999