# Jerusalem Mathematics Colloquium

Thursday, 13th May 2010, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Dmitry Jakobson

(McGill)

"Gauss curvature of random metrics"

** Abstract: **

We study Gauss curvature for random Riemannian metrics on a
compact surface, lying in a fixed conformal class; our questions are
motivated by comparison geometry. We explain how to estimate the
probability that Gauss curvature will change sign after a random
conformal perturbation
of a metric, and discuss some extremal problems for that probability,
and their relation to other extremal problems in spectral geometry.

If time permits, analogous questions will be considered for the scalar
curvature in dimension n>2, as well as other related problems
(e.g. Q-curvature in even dimensions).

This is joint work with Y. Canzani and I. Wigman.

Light refreshments will be served in the faculty lounge at 3:30.

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