We prove that if a Hamiltonian diffeomorphism of a closed monotone symplectic manifold
with semisimple quantum homology has more contractible fixed points, counted …

We develop a variant of Lusternik–Schnirelmann theory for the shift operator in equivariant
Floer and symplectic homology. Our key result is that the spectral invariants are strictly …

We construct a multiplicative spectral sequence converging to the symplectic cohomology
ring of any affine variety X, with first page built out of topological invariants associated to …

In this note we prove that if a closed monotone symplectic manifold $ M $ of dimension $2 n,
$ satisfying a homological condition that holds in particular when the minimal Chern number …

We study the symplectic cohomology of affine algebraic surfaces that admit a
compactification by a normal crossings anticanonical divisor. Using a toroidal structure near …

We show that the existence of one simple closed Reeb orbit of a particular type (a
symplectically degenerate maximum) forces the Reeb flow to have infinitely many periodic …

This is (mainly) a survey of recent results on the problem of the existence of infinitely many
periodic orbits for Hamiltonian diffeomorphisms and Reeb flows. We focus on the Conley …

We investigate the effect of a hyperbolic (or, more generally, isolated as an invariant set)
closed Reeb orbit on the dynamics of a Reeb flow on the $(2n-1) $-dimensional standard …

We show that Rabinowitz Floer homology and cohomology carry the structure of a graded
Frobenius algebra for both closed and open strings. We prove a Poincar\'e duality theorem …

On every closed contact manifold there exist contact forms with volume one whose Reeb
flows have arbitrarily small topological entropy. In contrast, for many closed manifolds there …