Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg–Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.
The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.
Lectures
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Floer Homology Fundamentals
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String Topology
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Floer Homotopy
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Spectra and Smash Products
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Floer Homology Applications
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Special: Problem Sessions
| Title | Speaker |
Date |
|---|---|---|
| Floer Homology Fundamentals 1 | Catherine Cannizzo | July 11, 2022 - 9:00am |
| Floer Homology Fundamentals 2 | Nate Bottman | July 11, 2022 - 1:00pm |
| Floer Homology Fundamentals 3 | Catherine Cannizzo | July 12, 2022 - 9:00am |
| String Topology 1 | Katherine Poirier | July 12, 2022 - 10:30am |
| Floer Homology Fundamentals 4 | Nate Bottman | July 12, 2022 - 1:00pm |
| Floer Homology Fundamentals 5 | Catherine Cannizzo | July 13, 2022 - 9:00am |
| String Topology 2 | Katherine Poirier | July 13, 2022 - 12:00pm |
| Floer Homology Fundamentals 6 | Nate Bottman | July 14, 2022 - 9:00am |
| String Topology 3 | Katherine Poirier | July 14, 2022 - 10:30am |
| Floer Homology Fundamentals 7 | Nate Bottman | July 14, 2022 - 1:00pm |
| Symplectomorphisms mirror to birational transformations of P^2 | Abigail Ward | July 14, 2022 - 4:30pm |
| Floer Homology Fundamentals 8 | Nate Bottman | July 15, 2022 - 9:00am |
| Floer Homology Fundamentals 9 | Catherine Cannizzo | July 15, 2022 - 1:00pm |
| Spectra and Smash Products 1 | Cary Malkiewich | July 18, 2022 - 9:00am |
| Floer Homotopy 1 | Mohammed Abouzaid | July 18, 2022 - 1:00pm |
| A knot Floer stable homotopy type | Ciprian Manolescu | July 18, 2022 - 2:30pm |
| Floer Homotopy 2 | Mohammed Abouzaid | July 19, 2022 - 9:00am |
| Floer Homotopy 3 | Mohammed Abouzaid | July 19, 2022 - 1:00pm |
| Spectra and Smash Products 2 | Cary Malkiewich | July 20, 2022 - 9:00am |
| Floer Homology Applications 1 | Jeff Hicks | July 20, 2022 - 10:30am |
| Floer Homotopy 4 | Mohammed Abouzaid | July 20, 2022 - 12:00pm |
| Spectra and Smash Products 3 | Cary Malkiewich | July 21, 2022 - 9:00am |
| Floer Homology Applications 2 | Jeff Hicks | July 21, 2022 - 1:00pm |
| The equivalence of the Ekeland-Hofer and equivariant symplectic homology capacities | Vinicius G. B. Ramos | July 21, 2022 - 4:30pm |
| Spectra and Smash Products 4 | Cary Malkiewich | July 22, 2022 - 9:00am |
| Floer Homology Applications 3 | Jeff Hicks | July 22, 2022 - 1:00pm |
