Homotopy Theory, Manifolds, and Field Theories

Explore advanced topics in algebraic topology and differential geometry through this comprehensive lecture series delivered during a trimester program at the Hausdorff Research Institute for Mathematics. Delve into three interconnected areas of modern mathematics: elliptic cohomology and its relationship to elliptic curves through Charles Rezk's four-part series, factorization homology as presented by David Ayala across three lectures, and the theory of moduli spaces of manifolds covered by Oscar Randal-Williams in three parts. Gain insights into cutting-edge research at the intersection of homotopy theory, manifold topology, and quantum field theory from leading experts in the field. Master fundamental concepts and recent developments in these sophisticated mathematical frameworks that bridge algebraic topology, algebraic geometry, and mathematical physics. Access high-level mathematical content suitable for graduate students and researchers working in topology, geometry, and related areas of pure mathematics.