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Presented By: Colloquium Series - Department of Mathematics

Colloquium Seminar: Random curves and surfaces

Nina Holden (Courant Institute/NYU)

How can you sample a surface uniformly at random? A natural approach is to consider a uniformly sampled planar map, which is a model for a discrete surface studied in many branches of both math and physics. When the size of the surface goes to infinity it converges to the continuum random surface known as a Liouville quantum gravity surface, which was originally introduced in the physics literature. We will give an introduction to these objects and present a powerful technique to study them known as conformal welding, where the random fractal curves known as Schramm-Loewner evolutions appear.

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