Seminar

The self-avoiding walk is a model of random walks on a lattice in which one only allows walks which do not intersect themselves. It is believed that in two dimensions this model should satisfy a form of conformal invariance, and the scaling limit should be the Schramm-Loewner evolution (SLE) with kappa=8/3. There are a variety of different senses in which the scaling limit should converge to SLE. I will review some of the well known conjectures and present some new conjectures. There are no proofs of any of these conjectures, but most of them are supported by Monte Carlo simulations.