GÖRAN
GUSTAFSSON Lectures
April 21 - 25, 2006
KTH, Stockholm
Speaker:
Wendelin Werner
Université Paris-Sud,
Ecole Normale Supérieure
The frontier of
Brownian motion
Abstract for the lecture series:
"Random planar objects and related questions"
The goal of these results is to present some of the recent mathematical ideas
that have improved our understanding of random planar conformally invariant
objects.
The first lecture will be of introductory nature and accessible to a wide
audience. We will say general things on macroscopic systems consisting of many
random microscopic inputs, discuss the difficulty to describe those systems
that exhibit randomness at macroscopic scale, and try to explain why those
systems that can be described mathematically are interesting objects, related
to other aspects of mathematics.
In the second lecture, I will introduce and discuss aspects of the Schramm-
Loewner Evolution that are random two-dimensional curves defined via
iterations of random conformal maps, and appear to be the only conformally
invariant models for two-dimensional interfaces.
In the final third lecture, I will describe special measures on planar random
loops, and their properties (conformal restriction properties
etc.)
Most of the content of these lectures will be based on joint work with Greg
Lawler and Oded Schramm.
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2006-01-03