Intrinsic Volumes and Gaussian Processes
Intrinsic volumes are renormalized versions of the classic quermassintegrals,
which play an important role in the theory of convex bodies, notably in
the Steiner volume formula and in a celebrated characterization theorem
of Hadwiger. More recently, they have been seen to have a remarkable
connection with Gaussian processes. This has led to novel insights in both
areas. Among these, I will discuss, as time permits: extension of intrinsic
volumes to infinite dimensional convex bodies, bounds and estimates for
Gaussian processes, Ito-Nisio oscillation and Gaussian black holes, the
Wills functional, and the Brownian motion body.
Seminar to be held in Room 107, 24 Hillhouse Avenue at 4:15 pm