Colloquium: Tuesday, November 2, 2021. Speaker: Dmitry Faifman (Tel Aviv). Title: “Intrinsic volumes and Weyl’s principle in valuation theory”.
Speaker: Dmitry Faifman (Tel Aviv University)
Date: Tuesday, November 2, 2021
Title: Intrinsic volumes and Weyl’s principle in valuation theory
Abstract: First we will recall the fundamental notion of intrinsic volumes, known as quermassintegrals in convex geometry. Those notions were extended later to Riemannian manifolds by H. Weyl, who discovered a remarkable fact: given a manifold M embedded in Euclidean space, the volume of the epsilon-tube around it is an invariant of the Riemannian metric on M. We then discuss Alesker’s theory of smooth valuations, which provides a framework and a powerful toolset to study integral geometry, in particular in the presence of various symmetry groups; we will see how Weyl’s theorem fits into this framework.
We then explore the various forms Weyl’s theorem assumes in various geometric settings, in particular in Lorentzian and Finslerian geometries.