Statistics Seminar Wednesday 4th August 2004

SUPREMA OF GAUSSIAN FIELDS, MAPPING THE BRAIN, AND MANIFOLDS

Speaker: Professor Robert J. Adler
Faculty of Industrial Engineering and Management
Technion, Haifa, ISRAEL

Time: 4:00p.m. Wednesday 4th August 2004

Venue: Old Main Building Room OMB-145A
near Barker Street Gate 14

I shall start by briefly discussing some statistical problems related to mapping the brain, both the cerebrum (the brain) and the
cerebral cortex, (the brain surface).

The next step will be to convince you that handling the cerebrum involves looking at an eight dimensional Whitney stratified manifold, while the cerebral cortex is only five dimensional. Along the way, I will explain what a Whitney stratified manifold is.
In the final step I will give the best solution to date (and perhaps the best possible) to finding sharp and practical estimates for the probability that the suprema of random fields over such manifolds exceeds given levels, a problem that has been around for over 70 years.

>From a historical point of view, these results provide a sort of closure to results of my 1976 UNSW PhD thesis. Maybe I should have got it all right back then, but then I wasn't working with Jonathan Taylor and Akimichi Takemura, who are
co-authors on the results of paragraph 3.