We construct “barcodes” for the chain complexes over Novikov rings that arise in Novikov's
Morse theory for closed one-forms and in Floer theory on not-necessarily-monotone …

We prove a conjecture of Viterbo from 2007 on the existence of a uniform bound on the
Lagrangian spectral norm of Hamiltonian deformations of the zero section in unit cotangent …

We investigate the relations between algebraic structures, spectral invariants and
persistence modules, in the context of monotone Lagrangian Floer homology with …

Our first main result states that the spectral norm γ γ on Ham (M, ω) Ham (M, ω), introduced
in the works of Viterbo, Schwarz and Oh, is continuous with respect to the C^ 0 C 0 topology …

Since spectral invariants were introduced in cotangent bundles via generating functions by
Viterbo in the seminal paper [73], they have been defined in various contexts, mainly via …

We identify a new class of closed smooth manifolds for which there exists a uniform bound
on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in a unit …

In the 1970s, Fathi, having proven that the group of compactly supported volume-preserving
homeomorphisms of the n-ball is simple for n≥3, asked if the same statement holds in …

We extend to higher dimensions the notion of Birkhoff attractor of a dissipative map. We
prove that this notion coincides with the classical Birkhoff attractor. We prove that for the …

In this paper we study submanifolds of contact manifolds. The main submanifolds we are
interested in are contact coisotropic submanifolds. Based on a correspondence between …

The Arnold conjecture states that a Hamiltonian diffeomorphism of a closed and connected
symplectic manifold (M, ω)(M, ω) must have at least as many fixed points as the minimal …