Peres, Y (Microsoft Research)
Tuesday 16 June 2015, 09:00-10:00

Competitive erosion is conformally invariant

A new frontier has emerged at the interface between probability, geometry, and analysis, with a central target to produce a coherent theory of the geometry of random structures. The principal question is the following: within a given structure, what is the interplay between randomness and geometry? More precisely, does the geometry appear to be random at every scale (i.e. fractal), or do fluctuations "average out" at sufficiently large scales? Can the global geometry be described by taking a suitable scaling limit that allows for concrete computations?

Spectacular progress has been made over the last ten years in this domain. The goal of the programme is to gather experts from probability, geometry, analysis and other connected areas, in order to study aspects of this question in some paradigmatic situations. Topics of particular relevance include the Gaussian Free Field, random planar maps and Liouville quantum gravity, in connection with conformally invariant scaling limits; spin glass models and branching random walks; percolation and random graphs; and random walks on graphs and groups in the case where the geometry is determined by some algebraic ambient structure.

Lévy, T (Pierre and Marie Curie University)
Tuesday 23 June 2015, 16:00 - 17:00

The master field in the plane

Alberts, T (University of Utah)
Thursday 18 June 2015, 16:30-17:30

Boundary Measures and Natural Time Parameterization for SLE

Burdzy, C (University of Washington)
Friday 19 June 2015, 10:00-11:00

Twin peaks

Beffara, V (ENS - Lyon)
Friday 19 June 2015, 14:00-15:00

From Internal DLA to self-interacting walks

Kang, N-G (Seoul National University)
Thursday 18 June 2015, 11:30-12:30

Competitive erosion is conformally invariant

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