3:00–4:00 pm Eckhart Hall, Room 202
Theory of Valuations on Manifolds
Abstract:
The notion of a valuation on a smooth manifold was introduced by the speaker, motivated by the classical concept of a valuation on convex sets (no prior familiarity with the latter is assumed in this talk).
A valuation is a finitely additive measure of a special form, defined on differentiable polyhedra in the manifold. Basic examples include classical (smooth) measures and the Euler characteristic.
The space of valuations on a manifold forms a topological filtered commutative algebra. The algebra of smooth functions appears as a quotient of this algebra, while the space of smooth measures forms a closed subspace.
The theory has applications in integral geometry, though we will not have time to discuss them in this talk. Instead, we will survey the structures and properties of the space of valuations.
April 30, 2025