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...
In this talk, I will first discuss some instances in which
orbifolds occur in geometry and dynamics, in particular, in the
context of billiards and systolic inequalities. Then I will present
topological conditions for an orbifold to be a manifold...
