Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

We introduce an equivariant Lagrangian Floer theory on compact symplectic toric manifolds. We define a spectral sequence to compute the equivariant Floer cohomology. We show that the set of pairs $(L,b)$, each consisting of a Lagrangian torus fiber...

Around twenty years ago Emmanuel Giroux formulated the equivalence of contact structures and open book decompositions with Weinstein pages up to stabilization. We establish the Giroux correspondence in full generality using the recent developments...

I will discuss how much the choice of coefficients impacts the quantitative information of Floer theory, especially spectral invariants. In particular, I will present some phenomena that are specific to integer coefficients, including an answer to a...

Strong inversions are a class of order-2 symmetries of knots in . Building on work of Seidel-Smith, Lidman-Manolescu, Stoffregen-Zhang, and others, we will describe a relationship between the Khovanov homology of a knot with a strong inversion and...

Given a Lagrangian torus fibration on the complement of an anticanonical divisor in a Kahler manifold, one usually constructs a mirror space by gluing local charts (moduli spaces of objects of the Fukaya category supported on generic torus fibers)...

An old open question in symplectic topology is whether all normalized capacities coincide on convex bounded domains in the standard symplectic vector space. I will discuss this question for domains which are close to the Euclidean ball and its...

I will discuss the relationship between positive loops of contactomorphisms of a fillable contact manifold and the symplectic cohomology (SH) of the filling. The main result is that the existence of a positive loop which is "extensible" implies SH...

A magnetic system is the toy model for the motion of a charged particle moving on a Riemannian manifold endowed with a magnetic force. To a magnetic flow we associate an operator, called the magnetic curvature operator. Such an operator encodes...

Dimitroglou-Rizell-Golovko constructs a family of Legendrians in prequantization bundles by taking lifts of monotone Lagrangians. These lifted Legendrians have a Morse-Bott family of Reeb chords. We construct a version of Legendrian Contact Homology...

The tangent bundle of a Kähler manifold admits in a neighborhood of the zero section a hyperkähler structure. From a symplectic point of view, this means we have three symplectic structures all compatible with a single metric. Two of the three...