## Steffen Rohde, University of Washington

Random conformal maps and SLE

**
Thursday April 27, 4:00PM,
Herman Brown 227**
In this talk, aimed at the non-expert,
I will describe a major breakthrough
in probability theory: Based on pioneering work
of Oded Schramm, it has been realized that a fairly
large class of random curves associated with critical
lattice processes from statistical physics can be
described by a simple differential equation,
the ``Schramm Loewner Evolution'' SLE, involving
conformal maps. Examples include percolation,
the loop erased random walk,
and conjecturally the self-avoiding walk and
the Ising model.
As a consequence, numerous ``predictions'' from
theoretical physics have been proved rigorously,
several conjectures (e.g. Mandelbrots conjecture
about the Hausdorff dimension of the ``Brownian frontier'') have been settled, and some outstanding problems (e.g. the size of self avoiding walks) moved within reach. I will also describe other families of random conformal maps, as well as open problems.