School of Mathematical Sciences
Monday, November 9, 2009
Schreiber 006, 12:15
From Statistics to Topology and back again
For motivation and to give us a concrete example, I shall start
by briefly discussing some problems arising in the statistical
analysis of brain images.
The next step will be to turn this into an abstract problem, of
considerable independent and intrinsic interest, related
to the topology of sets generated by Gaussian random processes
Out of this will come extensions to Riemannian manifolds of the
famous Kinematic Fundamental Formula of classical, Euclidean,
integral geometry, as well as new results related to (random)
In the end we shall see how these results shed new light on excursion
probabilities for smooth Gaussian processes, and even how they are
relevant to analysing brain images.
No background in either Gaussian processes or topology will be assumed.
Coffee will be served at 12:00 before the lecture
at Schreiber building 006