AMSI/ANZAMP AGR Symposium on probability in statistical mechanics: Phase transitions and conformal invariance within planar fractal carpets

17 January 2014, 11.30am AEDT

Speaker's Name:

Professor Wendelin Werner

Speaker's Institution:

ETH Zurich (Switzerland)

Title of Seminar:

Phase transitions and conformal invariance within planar fractal carpets

Host Institution:

AMSI

Time and Date:

Friday 17 January 2014, 11.30am AEDT

Seminar Abstract:

It is now known for a number of models of statistical physics in two dimensions (such as percolation or the Ising model) that at their critical point, they do behave in a conformally invariant way in the large-scale limit, and do give rise in this limit to random fractals that can be mathematically described via Schramm's Stochastic Loewner Evolutions.

The goal of the present talk will be to discuss some aspects of what remains valid or should remain valid about such models and their conformal invariance, when one looks at them within a fractal-type planar domain. We shall in particular describe (and characterize) a continuous percolation interface within certain particular random fractal carpets. Part of this talk will be based on joint work with Jason Miller and Scott Sheffield.

Speaker Bio:

Wendelin Werner (born September 23, 1968) is a German-born French mathematician working in the area of self-avoiding random walks, Schramm-Loewner evolution, and related theories in probability theory and mathematical physics. In 2006, at the 25th International Congress of Mathematicians in Madrid, Spain he received the Fields Medal. He is currently professor at ETH Zürich.

He has received other awards, including the Fermat Prize in 2001, the Loève Prize in 2005, and the 2006 SIAM George Pólya Prize with his collaborators Gregory Lawler and Oded Schramm. He was awarded the Rollo Davidson Prize in 1998 and is a trustee of the Rollo Davidson Trust. He became a member of the French Academy of Sciences in 2008.

He also had a part in the 1982 French film La Passante du Sans-Souci.

Seminar Convenor:

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