## S.I.G.M.A. Seminar

# Random Fields on Riemannian Manifolds: The Gaussian Kinematic Formula

## Marco Carfagnini

### Friday, October 12, 2018
12:20 pm

MONT 214 (Storrs)

The main goal of this talk is to provide a connection between geometry and probability in the setting of random elds. Random elds will be dened in a more geometric setting than the usual Euclidean space, and they can be viewed as natural generalizations of stochastic processes. Some historical and practical motivation also will be given. The main purpose is to study the geometry of the excursion set Au. To do that, a particular attention is given to the Gaussian kinematic formula. We will comment on this formula and, if time permits, give an outline of the proof and few (concrete) examples.