Rigidity Results for Initial Data Sets Satisfying the Dominant Energy Condition

Explore rigidity theorems for initial data sets in this mathematics research lecture that examines compact smooth spin manifolds with boundary and compact convex polytopes under the dominant energy condition (DEC). Learn about boundary value problems for Dirac operators and discover how they help identify extremal cases of initial data sets satisfying DEC in manifolds with smooth boundary. Delve into an extension of Gromov's polytope comparison framework for positive scalar curvature, seeing how it adapts to initial data sets through approximations by manifolds with smooth boundary. Based on collaborative research with C. Bär, S. Brendle, and B. Hanke, gain insights into these advanced mathematical concepts presented by MIT researcher Tsz-Kiu Aaron Chow at the Institut des Hautes Etudes Scientifiques.