# Program

The development of Floer theory in its early years can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the construction of algebraic structures on these homology groups and their underlying chain complexes. In continuing work that started in the latter part of the 20th century, algebraic topologists and homotopy theorists have developed deep methods for refining these constructions, motivated in large part by the application of understanding the classification of manifolds. The goal of this program is to relate these developments to Floer theory with the dual aims of (i) making progress in understanding symplectic and low-dimensional topology, and (ii) providing a new set of geometrically motivated questions in homotopy theory.
Bibliography

**Keywords and Mathematics Subject Classification (MSC)**

**Tags/Keywords**

Floer homology

equivariant

stable homotopy

spectrum

Lagrangian

symplectic manifold

Fukaya category

string topology

3-manifold

Seiberg-Witten

monopole

instanton

**Primary Mathematics Subject Classification**

**Secondary Mathematics Subject Classification**

55N91 - Equivariant homology and cohomology in algebraic topology [See also 19L47]

55P43 - Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.)

55P91 - Equivariant homotopy theory in algebraic topology [See also 19L47]

57M60 - Group actions on manifolds and cell complexes in low dimensions

57R57 - Applications of global analysis to structures on manifolds [See also 57K41, 58-XX]

September 08, 2022 - September 09, 2022 | [HYBRID WORKSHOP] Connections Workshop: Floer Homotopy Theory |

September 12, 2022 - September 16, 2022 | [HYBRID WORKSHOP] Introductory Workshop: Floer Homotopy Theory |

November 14, 2022 - November 18, 2022 | [HYBRID WORKSHOP] Floer Homotopical Methods in Low Dimensional and Symplectic Topology |