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Liouville quantum gravity as a mating of trees

Thursday 29th January 2015 - 09:00 to 10:00
INI Seminar Room 1
Co-authors: Bertrand Duplantier (CEA/Saclay), Scott Sheffield (Massachusetts Institute of Technology)

There is a simple way to “glue together” a coupled pair of continuum random trees to produce a topological sphere. The sphere comes equipped with a measure and a space-filling curve (which describes the “interface” between the trees). We present an explicit and canonical way to embed the sphere into the Riemann sphere. In this embedding, the measure is Liouville quantum gravity with parameter gamma in (0,2), and the curve is space-filling version of SLE with kappa=16/gamma^2. Based on joint work with Bertrand Duplantier and Scott Sheffield.

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