The Intrinsic Volumes of a Space Filling Diagram and Their Derivatives

Explore the morphological approach to modeling free energy in molecular dynamics through a 50-minute lecture by Herbert Edelsbrunner, presented by the Applied Algebraic Topology Network. Delve into the linear combination of weighted versions of four intrinsic volumes in space filling diagrams: volume, area, total mean curvature, and total Gaussian curvature. Learn about the Alpha shape representation of solid sphere unions and discover formulas for weighted intrinsic volumes and their derivatives. Gain insights into collaborative work with Robert Bryant, Patrice Koehl, and Michael Levitt on volume and area derivatives, as well as recent developments in mean and Gaussian curvature derivatives with Arseniy Akopyan.

Herbert Edelsbrunner: The intrinsic volumes of a space filling diagram and their derivatives