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Explore the algebraic structure of groups of area-preserving homeomorphisms in this lecture from the Simons Semester on Dynamics. Delve into Sobhan Seyfaddini's research on Albert Fathi's influential question regarding the simplicity of compactly supported volume-preserving homeomorphisms. Learn about the groundbreaking work that answers Fathi's question and settles the "simplicity conjecture" for the 2-disc. Discover the concept of "Hamiltonian homeomorphisms" and the numerical invariants called link spectral invariants that play a crucial role in solving Fathi's more general question about compact surfaces. Gain insights into the application of Lagrangian Floer homology and associated spectral invariants in this fascinating exploration of area-preserving maps and their properties.
