Workshop

This will be a hybrid workshop with in-person participation by members of the semester-long program and speakers. Online participation will be open to all who register.  Over the last decade, there has been a wealth of new applications of homotopy-theoretic techniques to Floer homology in low-dimensional topology and symplectic geometry, including Manolescu’s disproof of the high-dimensional Triangulation Conjecture and Abouzaid-Blumberg’s proof of the Arnol’d Conjecture in finite characteristic. Conversely, results in Floer theory and categorification have opened new directions of research in homotopy theory, from string topology to S-Lie algebras. The goal of this workshop is to introduce researchers in Floer theory to modern techniques and questions in homotopy theory and, conversely, introduce researchers in homotopy theory to ideas underlying Floer theory and its applications. The workshop will feature: - A Homotopy Theory lecture series by Anna Marie Bohmann and Alexander Kupers, aimed at symplectic geometers - A Floer Theory lecture series by Dusa McDuff and Chris Wendl, aimed at algebraic topologists - Paired hour talks on several subjects, connecting classical ideas to recent results:  (a) String topology by Oancea and Hingston (b) Infinity structures and operads by Bottman and Wilkins (c) Atiyah-Bott-Shapiro orientations and the Cohen-Jones-Segal construction by Klang and Kragh (d) Monopole Floer theory and homotopy theory by Lin, Shi, and Xu. - Moderated question-and-answer sessions about Floer theory and homotopy theory.