TALK BY R. ADLER, NOV 6, 2003

RANDOM FIELDS, BRAINS, AND MANIFOLDS
Robert J. Adler
Technion - Israel Institute of Technology
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.