Canada Research Chair in Differential Geometry and Topology

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This Chair aims at resolving one of the major gaps in our understanding of Open String theory. This theory has a mathematical counterpart, called Symplectic Topology, that constitutes the central focus of our Chair. Both of these theories appeared at the same time, but independently, in the 1980's, String Theory as a fantastic enterprise to unify the Quantum theory (infinitesimal scale) with General relativity (large scale), the dream of Einstein, while Symplectic Topology was born in response to deep problems of Hamiltonian mechanics. This Chair set up a long term research program to fill this gap, our Cluster Theory that has had, up to now, major successes. * The other focus of this Chair is the search for "Statistical Symplectic Topology", which concretely asks the question: "To which extent do the main rigidity features of Symplectic theory persist when one considers various limits related to the number of particles considered. This question becomes fascinating when one assigns to each particle a level of uncertainty in its measure and a principle of exclusion.