UW Probability Seminar
Next Seminar:
Time: Monday, May 19, 2008 at 2:30 pm.
Location: LOW 101
Speaker: Oded Schramm (Microsoft Research)
Title: Random metrics, the mathematics of quantum gravity
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Abstract:
In quantum gravity, the geometry of space itself is random.
One procedure to produce a random metric on a sphere is to fix some large $n$ and to
take the uniform distribution over all isometry classes of topological spheres that can
be obtained by pasting together side to side $n$ equilateral triangles of side-length
$1$.
These objects can be shown to be metrically $4$ dimensional in the large (though
topologically they are $2$ dimensional). One mathematical reason for the interest in
these random geometries stems from the KPZ formula, which is a prediction from physics
linking random processes on random geometries to conformally invariant random processes
in the plane. Amazingly, some questions turn out to be simpler in the random geometry
setting, and the KPZ formula has been used to make very specific conjectures about
random processes in the plane. Very recently, there has been a great deal of progress in
the mathematical understanding of the random geometries. I plan
to survey the subject.
Archive of previous talks
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