In the 1960s, V. Arnold conjectured that the minimum number of fixed points of a Hamiltonian diffeomorphism is bounded below by the topology of the symplectic manifold. This statement can be reformulated in terms of the minimum number of intersection points of two Lagrangian submanifolds. Hence, understanding the geometry and behavior of Lagrangian submanifolds is of fundamental importance in symplectic topology.
In this talk, I will offer an introductory overview of the main ideas behind the study of Lagrangian intersections and their role in understanding the broader structure of symplectic manifolds.
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