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Random geometry

12th January 2015 to 3rd July 2015

Organisers: Itai Benjamini (Weizmann Institute of Science), Nathanaël Berestycki (Cambridge), Jean-François Le Gall (Paris-Sud) and Scott Sheffield (Massachusetts Institute of Technology)

Scientific Advisory Committee: Geoffrey Grimmett (Cambridge), James Norris (Cambridge), Yuval Peres (Microsoft Research), Stanislav Smirnov (Geneva), Wendelin Werner (Paris, Orsay)

Programme Theme

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.


This programme is supported by

Final Scientific Report: 

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons