The duality long exact sequence relates linearised Legendrian
contact homology and cohomology and was originally constructed by
Sabloff in the case of Legendrian knots. We show how the duality
long exact sequence can be generalised to a relative...
In this talk we discuss the existence of a new type of rigidity
of symplectic embeddings coming from obligatory intersections with
symplectic planes. This is based on a joint work with P.
Haim-Kislev and R. Hind.
For a compact subset K of a closed symplectic manifold,
Entov-Polterovich introduced the notion of (super)heaviness, which
reveals surprising symplectic rigidity. When K
is a Lagrangian submanifold, there is a well-established
criterion for its...
In this talk, based on joint work with Gonzalo Contreras, I will
briefly sketch the proof of the existence of global surfaces of
section for the Reeb flows of closed 3-manifolds satisfying a
condition à la Kupka-Smale: non-degeneracy of the closed...
Lagrangian Floer theory is a useful tool for studying the
structure of the homology of Lagrangian submanifolds. In some
cases, it can be used to detect more- we show it can detect the
framed bordism class of certain Lagrangians and in
particular...
We discuss the relation between hypersurface singularities (e.g.
ADE, E˜6,E˜7,E˜8, etc) and spectral invariants, which are
symplectic invariants coming from Floer theory.
Filtered Lagrangian Floer homology gives rise to a barcode
associated to a pair of Lagrangians. It is well-known that
the lengths of the finite bars and the spectral distance are lower
bounds of the Lagrangian Hofer metric. In this talk we are...
Enumerative mirror symmetry is a correspondence between closed
Gromov-Witten invariants of a space X, and period integrals of a
family Y. One of the predictions of Homological Mirror Symmetry is
that the closed Gromov-Witten invariants can be...
Powerful homology invariants of knots in 3-manifolds have
emerged from both the gauge-theoretic and the symplectic kinds of
Floer theory: on the gauge-theoretic side is the instanton knot
homology of Kronheimer-Mrowka, and on the symplectic the...
We show that for any closed symplectic manifold, the number of
1-periodic orbits of any non-degenerate Hamiltonian is bounded from
below by a version of total Betti number over Z, which takes
account of torsions of all characteristics. The proof...
