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TALK BY R. ADLER, NOV 6, 2003
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**
RANDOM FIELDS, BRAINS, AND MANIFOLDS **

Robert J. Adler

Technion - Israel Institute of Technology

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I shall start by discussing some statistical problems related to mapping
the brain, both the cerebrum (a 3-dimensional object) and the cerebral
cortex, or "brain surface" (a 2-dimensional manifold in 3-dimensional
space).
This problem has motivated recent deep results describing the
geometry of Gaussian random fields on manifolds, which, via a detour
into
differential geometry, I shall describe in some detail, and then relate
back to the original problem.
I shall also show how to relate these results to relatives of the Weyl
tube formulae to determine extremal probabilities of processes and
fields. This turns out to be an elegant exercise in integral and
differential geometry.