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Explore the evolution and modern applications of Morse theory in this comprehensive mathematical lecture spanning a century of development. Begin with Marston Morse's foundational 1925 work, reframed through Witten's 1980s formalism that constructs chain complexes from critical points and gradient flow lines to compute ordinary homology. Discover Floer's revolutionary extensions that capture more sophisticated manifold information beyond ordinary homology through gradient flow trajectories. Examine contemporary advances in symplectic topology and Hamiltonian dynamics that drive current research directions in this fundamental area of differential topology and geometric analysis.
