
Ahlfors Lecture series
November 1819, 2013, Organizers: HT Yau and ST Yau
Harvard University, Science Center
Speaker and Program
Wendelin Werner (ETH Zürich)

November 18, 2013:
Lecture I 4:155:15 PM in SC Hall A

Random Planar Paths and Random Partitions in the plane
The first goal of this lecture is to give a heuristic introduction to
Oded Schramm's SLE processes, which are the random planar curves that arise
naturally in many different contexts. In the second part, we will look at
how to fragment naturally at random a planar domain into smaller pieces,
which will lead to the description of the cocalled Conformal Loop Ensembles.
In both these questions, complex analysis (conformal maps) turns out to
play a keyrole. The second half of this lecture will be based on work by and
with Scott Sheffield.

November 19, 2013:
Lecture II 4:155:15 PM in SC Hall D
 Random Mountains and Random Surfaces
We will give a brief introduction to Gaussian Free Field in twodimensions, which is the natural analog
of Brownian motion when one replaces onedimensional time by a twodimensional domain.
We will then describe some of its surprising features, and show how to relate it to Schramm's
SLE and to some Conformal Loop Ensembles. Most of the talk will be based on work by and with
Scott Sheffield, Jason Miller, Sam Watson and Hao Wu.

