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Explore the relationship between closed geodesics and the first Betti number in this 59-minute conference talk delivered by Marco Mazzucchelli from ENS-Lyon at the X Workshop on Conservative Dynamics and Symplectic Geometry. Delve into advanced mathematical concepts at the intersection of differential geometry and topology as part of this special 20th anniversary edition of the workshop held at IMPA in Rio de Janeiro, Brazil. Gain insights into how geometric properties of closed geodesics relate to topological invariants, specifically the first Betti number, which measures the number of independent one-dimensional holes in a topological space. Learn from expert analysis presented in a specialized mathematical conference setting focused on conservative dynamics, symplectic geometry, and their applications to Hamiltonian dynamics, contact geometry, Lagrangian systems, twist maps, integrable systems, and Aubry-Mather theory. Benefit from the workshop's leisurely format designed to facilitate deep mathematical discussions among experts in symplectic topology and related fields.
