## 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