Dmytro Yeroshkin (ULB) will speak in the geometry seminar on Tuesday 1 October 2019 at 11am in the Salle de Profs. Dmytro’s title is Manifolds with Density and Measure and his abstract is below.
Riemannian manifolds with measure, and more general metric spaces with measure have been studied under different guises for decades. In this talk I’ll present a new geometric approach to these spaces that introduces a torsion free affine connection, as opposed to a measure, as the fundamental object of study. This approach allows us to connect the notion of a manifold with measure and the Bakry-Emery notion of manifold with density. This allows us to extend the work on comparison results to the new case of negative synthetic dimension, as well as reveals a number of new structures for future study. This is joint work with Will Wylie and Lee Kennard.