We define a large new class of open symplectic manifolds, which includes all Conical
Symplectic Resolutions. They come with a pseudoholomorphic $\mathbb {C}^* $-action …

Abstract We compute the Hofer–Zehnder capacity of disc tangent bundles of the complex
and real projective spaces of any dimension. The disc bundle is taken with respect to the …

Mysterious Duality has been discovered by Iqbal, Neitzke, and Vafa (Adv Theor Math Phys
5: 769–808, 2002) as a convincing, yet mysterious correspondence between certain …

We prove that symplectic cohomology for open convex symplectic manifolds is invariant
when the symplectic form undergoes deformations which may be nonexact and …

We study the relationship between a homological capacity c SH+(W) for Liouville domains W
defined using positive symplectic homology and the existence of periodic orbits for …

We introduce the concept of k-(semi)-dilation for Liouville domains, which is a generalization
of symplectic dilation defined by Seidel-Solomon. We prove that the existence of k-(semi) …

We consider exact fillings with vanishing first Chern class of asymptotically dynamically
convex (ADC) manifolds. We construct two structure maps on the positive symplectic …

By a well-known theorem of Viterbo, the symplectic homology of the cotangent bundle of a
closed manifold is isomorphic to the homology of its loop space. In this paper, we extend the …

We explicitly construct a symplectomorphism that relates magnetic twists to the invariant
hyperk\" ahler structure of the tangent bundle of a Hermitian symmetric space. This …

We define Hamiltonian Floer homology with differential graded (DG) local coefficients for
symplectically aspherical manifolds. The differential of the underlying complex involves …