Homotopy theory and Floer homology

June 23 - June 27, 2025 Floer homology was introduced roughly forty years ago by Andreas Floer as an infinite-dimensional generalization of Morse homology, and since then it has become a major tool in fields like symplectic topology, dynamics and low dimensional topology. A natural question, anticipated by Floer and first seriously explored by Cohen-Jones-Segal in the mid 1990s, asks whether Floer homology can be interpreted as the singular homology of a space and whether there exist Floer versions of other cohomology theories. Cohen-Jones-Segal proposed an approach to this question by lifting Floer homology to a stable homotopy type. In the years following the original work of Cohen-Jones-Segal, these ideas lay mostly dormant in the symplectic community. However, there has been renewed progress in recent years, and the field is now undergoing rapid development. The goal of this conference is to bring together a diverse group of researchers interested in Floer homotopy theory, and more broadly the applications of homotopy theory to Floer theory, with the aim of disseminating the latest developments in the field and fertilizing new collaborations.