We resolve the long-standing problem of constructing the action of the operad of framed
(stable) genus-0 curves on Hamiltonian Floer theory; this operad is equivalent to the framed …

This is a book aimed at graduate students and researchers in symplectic geometry, based
on a course I taught in 2019. The primary message is that the base of a Lagrangian torus …

We compute the relative symplectic cohomology sheaf in degree $0 $ on the bases of nodal
Lagrangian torus fibrations on four dimensional symplectic cluster manifolds. We show that it …

The complex projective plane ℂ P 2 contains certain Lagrangian CW-complexes called
pinwheels, which have interesting rigidity properties related to solutions of the Markov …

We give a mathematically precise statement of the SYZ conjecture between mirror space
pairs and prove it for any toric Calabi-Yau manifold with the Gross Lagrangian fibration. To …

Let $(X,\omega) $ be a geometrically bounded symplectic manifold of dimension at least six.
We show that every open subset of $ X $ contains infinitely many Lagrangian tori which are …

Since the pioneering work of Kontsevich and Soibelman (in: The unity of mathematics,
Springer, Berlin, 2006), scattering diagrams have started playing an important role in mirror …

Consider R 2n with its standard symplectic structure! D Pdxi^ dyi. A prototypical question in
symplectic geometry is to ask whether one domain of R 2n symplectically embeds into …

For a compact set $ K $ with contact type boundary in a symplectic manifold $ M $ we
construct a spectral sequence from the local Floer homology of the Reeb orbits, as studied …

We prove that the Landau–Ginzburg superpotential of del Pezzo surfaces can be realized as
a limit of their hyperKähler rotation toward the large complex structure limit point. As a …