Tyler Helmuth (Bristol): The continuous-time lace expansion and its applications

The lace expansion is one of the primary tools for proving that
probability models in high dimensions have mean field behaviour. I
will explain the previous sentence by describing joint work in
progress with David Brydges and Mark Holmes in which we develop a
continuous time lace expansion. To motivate our methods I will
introduce a class of n-component field theories that are
generalizations of the Ising model of ferromagnetism. When n is zero,
one, or two we are able to analyze these models. Our results for the
case $n=2$ are new.