The Grosse-Wulkenhaar model is the first perturbative renormalizable
quantum field theoriy defined on the 4 dimensional Moyal space.
In this talk I shall talk about the constructive renormalization the
model on 2-dimensional Moyal plane with the method of loop vertex
expansion. We treat renormalization with this new tool, adapt Nelson's
argument and prove Borel summability of the perturbation series.
This is the first non-commutative quantum field theory
model to be built in a non-perturbative sense.
Joel Lebowitz Rutgers University
Three easy (to state) open problems (that have worried me for many years)