Jonghyeon Ahn - Barcode entropy and relative symplectic cohomology

In this talk, I will discuss the barcode entropy—the exponential growth rate of the number of not-too-short bars—of the persistence module associated with the relative symplectic cohomology SH_M(K) of a Liouville domain K embedded in a symplectic manifold M. The main result establishes a quantitative link between this Floer-theoretic invariant and the dynamics of the Reeb flow on the boundary of K. More precisely, I will explain that the barcode entropy of the relative symplectic cohomology SH_M(K) is bounded above by a constant multiple of the topological entropy of the Reeb flow on the boundary of the domain, where the constant depends on the embedding of K into M.

Youngjin Bae - Monotone Lagrangian tori and exact Lagrangian fillings

Monotone Lagrangian submanifolds play a central role in the study of closed symplectic manifolds, particularly in the contexts of mirror symmetry and cluster algebras. On the other hand, exact Lagrangian fillings of Legendrian submanifolds serve as important objects in the study of Weinstein manifolds. In this talk, we explore a correspondence between monotone Lagrangian tori and exact Lagrangian fillings by examining smoothed divisor complements of toric 4-manifolds. We also compare almost toric mutation and Legendrian mutation in concrete examples. This is a joint project with Orsola Capovilla-Searle.

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.

Jean Gutt - Periodicity characterization by capacities for star-shaped domains

We will give a recent result about the spectral characterization of Besse and Zoll Reeb flows on the standard contact sphere S^{2n−1} initiated by Ginzburg–Gürel-Mazzucchelli. Roughly speaking, it states that a Reeb flow on the boundary of any star-shaped domain in R^{2n} is Besse if and only if it has n coinciding Ekeland–Hofer capacities, and that it is Zoll if and only if the first n capacities coincide. This is joint work with Shira Tanny and Vinicius Ramos.

Seongchan Kim - Time-dependent Stark-Zeeman systems and Floer homology

Stark-Zeeman systems arise naturally in celestial mechanics and provide a rich class of Hamiltonian systems that exhibit intricate dynamical behaviour. In this talk, we study time-dependent Stark-Zeeman systems from the viewpoint of symplectic geometry. After introducing these systems, we explain a regularisation procedure, due to Barutello-Ortega-Verzini, that resolves collision singularities and allows the dynamics to be described on a regularised phase space. A striking feature of the regularised system is that the resulting Hamiltonian equations involve delay-type terms. As a consequence, the corresponding Floer equation becomes non-local, and the standard analytical framework of Floer homology is no longer directly applicable. This indicates that new analytical tools are required in order to develop a Floer-theoretic approach to these systems. Motivated by this observation, we outline a program aimed at constructing a Floer homology theory adapted to time-dependent Stark-Zeeman systems.

Sangjin Lee - On the compact Fukaya category of plumbings. 

Ganatra–Pardon–Shende established a framework computing wrapped Fukaya category, by employing the local–to–global approach. In this talk, we will discuss how to study the "compact" Fukaya category of a Weinstein manifold, by utilizing the approach/result of Ganatra–Pardon–Shende. As the consequence, we can find some specific compact Lagrangians in plumbing spaces (our example space), which generate the compact Fukaya category. 

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.

Jun Zhang - Geometry and dynamics of domains in the cotangent bundle of tori

In Euclidean spaces, star-shaped domains (also known as Liouville domains) are fundamental objects in modern symplectic geometry. Several important subclasses have been introduced and studied, including dynamically convex domains, geometrically convex domains, and toric domains. These classes are not only interesting in their own right but also exhibit deep interrelations with one another. In this talk, we extend this discussion to (fiberwise) star-shaped domains in the cotangent bundles of tori. In particular, we introduce analogous subclasses in this new setting and explore classical topics such as large-scale geometric properties and embedding problems. This talk is based on joint work with Antong Zhu.

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.