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 lowdimensional 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 AbouzaidBlumberg's use of Floer homotopy theory and Morava Ktheory 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

Floer Homology Fundamentals

String Topology

Floer Homotopy

Spectra and Smash Products

Floer Homology Applications

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 EkelandHofer 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 