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Schedule The schedule is updated throughout the semester.
| Date | Speaker | Institution | Title |
|---|---|---|---|
| Nov 12, 2025 | Dustin Connery-Grigg | Institut de mathématiques de Jussieu – Paris Rive Gauche, Sorbonne Université | The geometry and topology of Hamiltonian Floer theory on surfaces |
| Nov 19, 2025 | Patricia Sorya | Université d'Ottawa | On the number of shared Dehn surgeries between two knots |
Abstracts
Date Nov 12, 2025
Speaker Dustin Connery-Grigg
Title The geometry and topology of Hamiltonian Floer theory on surfaces
Abstract Given a Hamiltonian dynamical system on a symplectic manifold, what is the relationship between the dynamical features which the system exhibits, and the topology of the underlying manifold? In 1989, Andreas Floer introduced a way to do relative Morse theory with the Hamiltonian action functional, and thereby answered a long-standing conjecture due to Arnol'd on relating the number of necessary fixed points to the underlying topology. Floer theory has since become ubiquitous in modern symplectic topology. Unfortunately, it is generally very difficult to understand how the Floer theory of a given Hamiltonian relates to the system's broader qualitative dynamics. In this talk, I will give a brief introduction to Floer's theory, and discuss some results in low-dimensions which provide links between the qualitative dynamics of low-dimensional Hamiltonian systems and their associated Floer theory.
Date Nov 19, 2025
Speaker Patricia Sorya
Title On the number of shared Dehn surgeries between two knots
Abstract Dehn surgery along a knot in the 3-sphere is one of the simplest ways to construct 3-manifolds. It is performed by gluing a solid torus to the exterior of the knot according to a rational parameter p/q. A folklore theorem states that for any pair of distinct knots, performing p/q-Dehn surgery on each knot yields homeomorphic manifolds for at most finitely many slopes p/q. In this talk, we discuss a proof based on the JSJ decomposition of knot exteriors. In particular, it provides an effective bound on the maximal number of shared surgeries between any two given knots.
If you have questions about the seminar, please direct them to Mike Wong, at Mike [dot] Wong [at] uOttawa [dot] ca.