Unni Namboodiri Lectures in Geometry and Topology - Autumn 2025 - Lecture 1 скачать в хорошем качестве

Unni Namboodiri Lectures in Geometry and Topology - Autumn 2025 - Lecture 1

Lecture 1: Cotangent Bundles and the Hopf Map - Mohammed Abouzaid (Stanford) Symplectic Topology 40 years after Floer The subject of symplectic topology has its roots in Poincare's attempts to understand qualitative properties of Hamiltonian dynamical systems, which at the time were only successful in low dimensions. It was not until the work of Gromov and Floer in the 1980's that the tools to extend Poincare insights to higher dimensions became available. Since then, these have been combined with ever more sophisticated algebraic structures, leading to the resolution of many long-open problems, such as the determination of the homotopy types of Lagrangian submanifolds in many classes of examples. These lectures will address the development of the last five years, during which the subject has shifted to combine methods of homotopy theory with generalisations of Morse theory, leading to new questions in both areas.