Abstract: 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 on manifolds.

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) persistent homologies.

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