### Wendelin Werner

Born 23 September 1968, Cologne (Germany)

Fields Medal (2006) “for his contributions to the development of stochastic Loewner evolution, the geometry of two-dimensional Brownian motion, and conformal field theory”

Wendelin Werner was born in Germany, but has had French citizenship since 1977. He studied at the École Normale Supérieure in Paris and was awarded his Ph.D. in 1993 by the University of Pierre and Marie Curie. From 1991 to 1997 he was researcher at the Centre National de la Recherche Scientifique (CNRS) in Paris, with a break of two years as a Leibniz Fellow at Cambridge University from 1993 to 1995.

He became professor of Mathematics at the Université Paris-Sud in Orsay in 1997 (did also teach at Ecole Normale Supérieure from 2005 to 2013), and is since 2013 professor at the ETH in Zürich. He has had several visiting professorship, including at Cambridge University and at TU Berlin as an Einstein fellow.

In his spare time he plays the violin and enjoys music and theatre.

Werner was awarded the Fields Medal in addition to numerous other awards, including the Rollo Davidson Prize (1998), the Prize of the European Mathematical Society (2000), the Fermat Prize (2001), the Jacques Herbrand Prize (2003), the Loève Prize (2005), and the Pólya Prize (2006).

Wendelin Werner works in probability theory at the interface between stochastics, analysis, and (statistical) physics. Among other things, he deals with random continuous structures that occur in the plane. More precisely, together with Gregory Lawler and Oded Schramm, he deepened our understanding of those systems which are conjectured (and now sometimes proved) to behave in a ‘conformally invariant way’ (this roughly means that when one distorts the law of the random image remains unchanged if one distorts it under an angle-preserving (‘conformal’) transformation). The tools that they use to understand these question combine stochastic analysis with complex analysis, and in particular the so-called Schramm-Loewner evolution, invented by Oded Schramm (1961-2008).

Among the results that Wendelin Werner and his coauthors obtained, one can for instance mention the conformal invariance of the uniform spanning tree model (with Lawler and Schramm), the value of critical exponents for critical percolation (with Lawler, Schramm, and also Smirnov), or the proof (with Lawler and Schramm) of the following conjecture by Benoit Mandelbrot (1924-2010): Consider a finite planar random path (generated by a Brownian motion), then it separates in the plane an infinite area from a finite one by a boundary line with fractal dimension equal to 4/3.