Paul Biran

Rigidity and uniruling for Lagrangian submanifolds

This paper explores the topology of monotone Lagrangian submanifolds

Propagation in Hamiltonian dynamics and relative symplectic homology

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Lagrangian barriers and symplectic embeddings

inside a symplectic manifold

CALABI QUASIMORPHISMS FOR THE SYMPLECTIC BALL

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Constructing new ample divisors out of old ones

by exploiting the relationships between the quantum homology of

LAGRANGIAN EMBEDDINGS INTO SUBCRITICAL STEIN MANIFOLDS

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From Symplectic Packing to Algebraic Geometry and Back

and various quantum structures associated to the Lagrangian

Lagrangian cobordism. I

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Connectedness of spaces of symplectic embeddings

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A Floer–Gysin exact sequence for Lagrangian submanifolds

The main result asserts the existence of noncontractible periodic orbits for compactly supported time dependent Hamiltonian systems on the unit cotangent bundle of the torus or of a negatively curved manifold whenever the generating Hamiltonian is sufficiently large over the zero section. The proof is based on Floer homology and on the notion of a relative symplectic capacity. Applications include results about propagation properties of sequential Hamiltonian systems, periodic orbits on hypersurfaces, Hamiltonian circle actions, and smooth Lagrangian skeletons in Stein manifolds.