Yuan Gao - Rabinowitz Fukaya categories and relative Calabi-Yau structures

Rabinowitz Floer homology bridges symplectic cohomology and symplectic homology. However, lifting its known cohomology-level dualities in the open-string sector to a chain-level categorical framework presents significant technical challenges. Specifically, the morphism spaces of the Rabinowitz Fukaya category naturally behave as Tate modules, which lack the abelian symmetric monoidal structure required for traditional homological algebra. In this talk, we resolve these difficulties by lifting the Rabinowitz Fukaya category to an enriched category over ultrasolid modules. Using a continuous, circle-equivariant open-closed map, we establish a strong right Calabi-Yau structure on this enriched category, along with a corresponding relative right Calabi-Yau structure on the canonical functor from the wrapped Fukaya category. Based on joint work-in-progress with Hanwool Bae.

Han Lou - On the Hofer-Zehnder conjecture for semipositive symplectic manifolds

Arnold conjecture says that the number of 1-periodic orbits of a Hamiltonian diffeomorphism is greater than or equal to the dimension of the Hamiltonian Floer homology. In 1994, Hofer and Zehnder conjectured that there are infinitely many periodic orbits if the equality doesn’t hold. In this talk, I will show that the Hofer-Zehnder conjecture is true for semipositive symplectic manifolds with semisimple quantum homology. This is a joint work with Marcelo Atallah.

Zhengyi Zhou - On symplectic CP^n 

We show that the existence of a pseudo-holomorphic line passing through two generic points on a symplectic manifold X, phrased using Gromov-Witten invariants, implies that X is homotopy equivalent to CP^n with identical first Chern class and small quantum cohomology. We then deduce some rigidity results regarding symplectic hyperplanes in CP^{n+1}. The proof is based on Rabinowitz Floer homology.