Seminars Sorted by Series

In this talk, we start by reviewing recent results on the dynamics of Reeb vector fields defined by contact forms on three-dimensional manifolds, and then introduce Reeb fields defined by stable Hamiltonian structures. These are more general and...

The Hofer’s metric dH is a remarkable bi-invariant metric on the group of Hamiltonian diffeomorphisms of a symplectic manifold. In my talk, I will explain a result, obtained jointly with Matthias Meiwes, which says that the braid type of a set of...

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...

We show that for any closed symlectic 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...

The basic invariant of a fixed point of a Hamiltonian diffeomorphism, besides its existence (which is implied by the proven Arnol'd Conjecture), is the number of eigenvalues of unit norm of the linearization of the map at the fixed point. When there...

David White (North Carolina State University):  Symplectic Instanton Homology of Knots and Links in 3-manifolds

Powerful homology invariants of knots in 3-manifolds have emerged from both the gauge-theoretic and the symplectic kinds of Floer theory...

We discuss the relation between hypersurface singularities (e.g. ADE, $\widetilde{E}_{6},\widetilde{E}_{7},\widetilde{E}_{8}$, etc) and spectral invariants, which are symplectic invariants coming from Floer theory.

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...

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...

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 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.

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...

Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula. The coefficients in this formula are calculated combinatorially using attractor flow trees. In joint...

Brayan Ferreira (Instituto de Matemática Pura e Aplicada): 

Gromov Width of Disk Cotangent Bundles of Spheres of Revolution: The question of whether a Symplectic manifold embeds into another is central in Symplectic topology. Since Gromov...

Given a convex billiard table, one defines the set $\mathcal{M}$ swept by locally maximizing orbits for convex billiard. This is a remarkable closed invariant set which does not depend (under certain assumptions) on the choice of the generating...

A symplectic embedding of a disjoint union of domains into a symplectic manifold M is said to be of Kahler type (respectively tame) if it is holomorphic with respect to some (not a priori fixed) integrable complex structure on M which is compatible...

The Toda lattice is one of the earliest examples of non-linear completely integrable systems. Under a large deformation, the Hamiltonian flow can be seen to converge to a billiard flow in a simplex. In the 1970s, action-angle coordinates were...

(This is a somewhat old-fashioned talk.) I will review the definition of symplectic cohomology and its deformation, for the complement of a smooth anticanonical divisor in a monotone symplectic manifold. The deformed group, with the parameter q...

While convex hypersurfaces are well understood in 3d contact topology, we are just starting to explore their basic properties in high dimensions. I will describe how to compute contact homologies (CH) of their neighborhoods, which can be used to...

Lukas Nakamura (University of Upsala):

A Metric on the Contactomorphism Group of an Orderable Contact Manifold: We discuss some properties of a pseudo-metric on the contactomorphism group of a strict contact manifold M induced by the maximum/minimum...

Spectral invariants defined via Embedded Contact Homology (ECH) or the closely related Periodic Floer Homology (PFH) satisfy a Weyl law: Asymptotically, they recover symplectic volume. This Weyl law has led to striking applications in dynamics...

Given a grid diagram for a knot or link in the three-sphere, we construct a spectrum whose homology is the knot Floer homology of . We conjecture that the homotopy type of the spectrum is an invariant of . Our construction does not use holomorphic...

The C0 distance on the space of contact forms on a contact manifold has been studied recently by different authors. It can be thought of as an analogue for Reeb flows of the Hofer metric on the space of Hamiltonian diffeomorphisms. In this talk, I...

• Julien Dardennes:The Coarse Distance from Dynamically Convex to Convex:

  Chaidez and Edtmair have recently found the first examples of dynamically convex domains in $R^4$ that are not symplectomorphic to convex domains, answering a long-standing open...

I will discuss how to build small symplectic caps for contact manifolds as a step in building small closed symplectic 4-manifolds. As an application of the construction, I will give explicit handlebody descriptions of symplectic embeddings of...

Floer homotopy type refines the Floer homology by associating a (stable) homotopy type to an Hamiltonian, whose homology gives the Hamiltonian Floer homology. In particular, one expects the existing structures on the latter to lift as well, such as...

• Francesco Morabito:Hofer Norms on Braid Groups and Quantitative Heegaard-Floer Homology

  Given a lagrangian link with k components it is possible to define an associated Hofer norm on the braid group with k strands. In this talk we are going to...

I will discuss a recursive formula for the homotopy type of the space of Legendrian embeddings of sufficiently positive cables with the maximal Thurston-Bennequin invariant. Via this formula, we identify infinitely many new components within the...

• Johanna Bimmermann :From Magnetically Twisted to Hyperkähler 

  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...

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...

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...

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)...

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...

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...

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...

• Yao Xiao : Equivariant Lagrangian Floer Theory on Compact Toric Manifolds

  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...

• Yan-Lung Leon Li :Equivariant Lagrangian Correspondence and a Conjecture of Teleman

  It has been a continuing interest, often with profound importance, in understanding the geometric and topological relationship between a Hamiltonian G-manifold Y and...

An old question of Poincaré concerns creating periodic orbits via perturbations of a flow/diffeomorphism. While pseudoholomorphic methods have successfully addressed this question in dimensions 2-3, the higher-dimensional case remains less...

In this talk, we will consider a stabilized version of the fundamental existence problem of symplectic structures (cf. Open Problem 1 in McDuff & Salamon). Given a formal symplectic manifold, i.e. a closed manifold $M$ with a non-degenerate 2-form...

The presence of hyperbolic periodic orbits or invariant sets often has an affect on the global behavior of a dynamical system. In this talk we discuss two theorems along the lines of this phenomenon, extending some properties of Hamiltonian...

We discuss constraints on exact Lagrangian embeddings obtained from considering bordism classes of flow modules over Lagrangian Floer flow categories. This talk reports on joint work with Noah Porcelli.

For the past 25 years, Legendrian contact homology has played a key role in contact topology. I'll discuss a package of new invariants for Legendrian knots and links that builds on Legendrian contact homology and is derived from rational symplectic...

Toric integrable systems, also known as symplectic toric manifolds, arise as examples in different contexts within geometry and related areas. Semitoric integrable systems are a generalization of toric integrable systems in dimension four. In this...

It is conjectured that every Reeb flow on a closed three-manifold has either two, or infinitely many, simple periodic orbits. I will survey what is currently known about this conjecture. Then, I will try to explain some of the key ideas behind...

Chen and Ruan constructed symplectic orbifold Gromov-Witten invariants more than 20 years ago.  In ongoing work with Alex Ritter, we show that moduli spaces of pseudo-holomorphic curves mapping to a symplectic orbifold admit global Kuranishi charts...

Given a path-connected topological space X, a differential graded (DG) local system (or derived local system) is a module over the DGA of chains on the based loop space of X. I will explain how to define in the symplectically aspherical case...

Associated to a star-shaped domain in $\mathbb{R}^{2n}$ are two increasing sequences of capacities: the Ekeland-Hofer capacities and the so-called Gutt-Hutchings capacities. I shall recall both constructions and then present the main theorem that...

• Adrien Currier (Université de Nantes) :Exact Lagrangians in Cotangent Bundles with Locally Conformally Symplectic Structure

  First considered by Lee in the 40s, locally conformally symplectic (LCS) geometry appears as a generalization of symplectic...

We show that two generic, open, convex or concave toric domains in $R^4$ are symplectomorphic if and only if they agree up to reflection. The proof uses barcodes in positive $S^1$-equivariant symplectic homology, or equivalently in cylindrical...