How Hard is the Theorem of Stolz - Metrics and Scalar Curvature in Spin Manifolds

Explore a mathematical lecture that delves into the complexity of Stolz's theorem and its implications for positive scalar curvature metrics on simply connected spin manifolds. Learn about the foundational work of Gromov–Lawson and Atiyah–Singer–Lichnerowicz–Hitchin, and discover how their contributions led to Stolz's breakthrough in determining which manifolds support these metrics. Examine the challenges involved in metric deformation and complexity through collaborative research findings presented by Fedor Manin from the University of Toronto, working alongside Shmuel Weinberger, Zhizhang Xie, and Guoliang Yu. Gain insights into the mathematical intricacies of transforming given metrics into those with positive scalar curvature and understand the complexities involved in finding deformations between different metric states.