Weighted Versions of Scalar Curvature, Mass and Spin Geometry for Ricci Flows

Watch a technical mathematics lecture from Harvard CMSA's General Relativity Workshop where MIT researcher Tristan Ozuch explores weighted versions of scalar curvature, mass and spin geometry in relation to Ricci flows. Learn about a newly defined Perelman-like functional for ALE metrics developed with A. Deruelle that examines the stability of Ricci-flat ALE metrics. Discover how classical objects and formulas from scalar curvature, spin geometry and general relativity extend to manifolds with densities through work done with J. Baldauf. Understand the surprising finding that ADM mass extension opposes the introduced functional, and how this functional equals a weighted spinorial Dirichlet energy on spin manifolds through a weighted Witten's formula. Explore how Ricci flow serves as the gradient flow for these mathematical quantities in this hour-long advanced mathematics presentation.