Event
Egor Shelukhin, Universit茅 de Montr茅al
Persistence modules in symplectic topology
In order to resolve Vladimir Arnol'd's famous conjecture from the 1960's, giving lower bounds on the number of fixed points of Hamiltonian diffeomorphisms of a symplectic manifold, Andreas Floer has associated in the late 1980's a homology theory to the Hamiltonian action functional on the loop space of the manifold. It was known for a long time that this homology theory can be filtered by the values of the action functional,聽聽yielding information about聽metric invariants in symplectic topology (Hofer's metric,聽 for example). We discuss a recent marriage between the filtered version of Floer theory and persistent homology, a new field of mathematics that has its origins in data analysis, providing examples of new ensuing results.