Daniel Spector - The Geometry of Spaces of Measures

The space of finite Radon measures is a somewhat natural choice in the modeling of physical phenomena: it has a simple mathematical structure; the norm on this space can be interpreted as the mass of the physical quantity that a given measure represents; bounded sequences admit weak-star compactness through the identification of this space with the dual of the space of continuous functions which decay at infinity. Two main caveats to its use, however, are its failure to support a strong-type Sobolev inequality and its lack of stability with respect to dimensional estimates.  In this talk we discuss these properties of measures in contrast to the Hardy space, and through this discussion move to a dialectical resolution: the dimension stable spaces of measures.  This talk is based on joint work with Dmitriy Stolyarov and Riju Basak.