Coursera Spring Sale
40% Off Coursera Plus Annual!
Grab it
Explore the foundations of symplectic topology in this advanced mathematics lecture delivered by Mohammed Abouzaid from Stanford University. Delve into cotangent bundles and the Hopf map as part of a comprehensive examination of symplectic topology's evolution over the past 40 years since Floer's groundbreaking contributions. Discover how this field emerged from Poincaré's early attempts to understand qualitative properties of Hamiltonian dynamical systems, which were initially limited to low-dimensional cases. Learn about the revolutionary developments in the 1980s when Gromov and Floer introduced tools that extended Poincaré's insights to higher dimensions. Examine how these foundational methods have been enhanced with increasingly sophisticated algebraic structures, enabling the resolution of numerous long-standing problems, including the determination of homotopy types of Lagrangian submanifolds across various classes of examples. Understand the recent five-year developments that have transformed the field by combining homotopy theory methods with generalizations of Morse theory, creating new research questions in both areas. This lecture serves as the opening session of the prestigious Unni Namboodiri Lectures series, providing essential background for understanding modern approaches to symplectic topology and its applications in geometry and topology.
