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Explore the action of fixed points and spectral invariants of Hamiltonian homeomorphisms of surfaces in this conference talk delivered by Vincent Humilière from Sorbonne Université Paris. Delve into advanced concepts in symplectic geometry and conservative dynamics as part of the X Workshop on Conservative Dynamics and Symplectic Geometry, a special 20th anniversary edition celebrating two decades of this prestigious mathematical meeting. Learn about cutting-edge research in symplectic topology with applications to Hamiltonian dynamics, contact geometry, dynamics of Lagrangian systems and twist maps, integrable systems, and Aubry-Mather theory. Gain insights from this expert presentation delivered at the Instituto de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil, where leading mathematicians from Brazil and abroad gather to discuss the latest developments in these interconnected fields of mathematics. Discover how spectral invariants provide powerful tools for understanding the dynamics of Hamiltonian systems on surfaces, and examine the relationship between fixed point theory and symplectic geometry in this specialized mathematical context.
