Mohammed Abouzaid: Bordism and Floer Theory

Explore the groundbreaking advances in low dimensional and symplectic topology through this 50-minute lecture by Mohammed Abouzaid at the Hausdorff Center for Mathematics. Delve into Andreas Floer's revolutionary discovery from the late 1980s, which extended Morse theory to an infinite dimensional setting where standard variational calculus methods fail. Examine the recent progress made in addressing the foundational difficulties that hindered the incorporation of generalized homology theory into Floer's work. Learn about two key developments: the creation of concrete models for Floer theory moduli spaces using equivariant vector bundles, and the geometric implications of elevating Floer homology to generalized homology theories. Conclude by understanding how the concept of derived orbifold bordism serves as a universal framework for Floer's invariants and their descendants, bridging the gap between bordism and Floer theory.