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Liouville quantum gravity and the Brownian map

Presented by: 
J Miller Massachusetts Institute of Technology
Monday 15th June 2015 - 14:00 to 15:00
INI Seminar Room 1
Co-author: Scott Sheffield (MIT)

Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has roots in string theory and conformal field theory. The second is the Brownian map, which has roots in planar map combinatorics. We show that the Brownian map is equivalent to Liouville quantum gravity with parameter $\gamma = \sqrt{8/3}$.

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