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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 Fathi's question regarding the simplicity of the group of compactly supported area-preserving homeomorphisms of the 2-disc. Learn about the negative answer to this question and its implications for the "simplicity conjecture." Discover the broader context of Fathi's inquiry into the simplicity of "Hamiltonian homeomorphisms" on compact surfaces. Examine the role of link spectral invariants in resolving these questions and gain insights into the construction of these numerical invariants using Lagrangian Floer homology. This lecture builds upon previous discussions, focusing on the application of link spectral invariants to solve Fathi's question and setting the stage for future explorations of Lagrangian Floer homology and its associated spectral invariants.
