# The 2013/14 Collingwood Lecture

** **Professor Wendelin Werner (ETH Zurich)

#### Fields Medallist 2006

#### "Randomness and the continuum"

Professor Wendelin Werner is one of the 2006 recipients of the Fields Medal, `for his
contribution to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and
conformal field theory'.

The Fields Medal, officially known as the International Medal for Outstanding
Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each
International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The
Fields Medal is often viewed as the greatest honour a mathematician can receive. The Fields Medal and the Abel Prize
have often been described as the `mathematician's Nobel Prize'.

**Abstract:** One can have a rather intuitive perception of the fact that space and time can be continuous, which is very directly related to the mathematical notion of continuity of functions. On the other hand, when one thinks of random phenomena, the natural examples that first come to mind are of discrete nature, such as coin tossing. The conceptual question of how "randomness" can be split up into and reassembled from infinitesimal little pieces turns out to be quite tricky. It is related to contemporary research in mathematics that we shall illustrate via some concrete examples.