Quebec Mathematical Sciences Colloquium

February 9, 2018 from 16:00 to 18:00 (Montreal/EST time) On location

Persistence modules in symplectic topology

Colloquium presented by Egor Shelukhin (Université de Montréal, Canada)

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, yielding information about metric invariants in symplectic topology (Hofer's metric, 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.


UQAM, Pavillon Président-­Kennedy, 201, ave du Président-­Kennedy, room PK­5115