Seminars Sorted by Series

The topic of the talk will be Floer theories on exact symplectic orbifolds with smooth contact boundary. More precisely, I will first describe the construction, which only uses classical transversality techniques, of a symplectic cohomology group on...

I will discuss joint work with McLean and Smith, lifting the results of Seidel, Lalonde, McDuff, and Polterovich concerning the topology of Hamiltonian fibrations over the 2-sphere from rational cohomology to complex cobordism. In addition to the...

This is joint work with Agustin Moreno and Dayung Koh. The restricted three-body problem is invariant under various antisymplectic involutions. These real structures give rise to the notion of symmetric periodic orbits which simultaneously have a...

Wenyuan Li (Northwestern), Estimating Reeb chords using microlocal sheaf theory

We show that, for closed Legendrians in 1-jet bundles, when there is a sheaf with singular support on the Legendrian, then (1) its self Reeb chords are bounded from...

I will discuss some quantitative aspects for Legendrians in a (more or less) general contact manifold. These include lower bounds on the number of Reeb chords between a Legendrian and its contact Hamiltonian image, the non-degeneracy of the Chekanov...

A compact four dimensional completely integrable system $f: M \to R^2$ is semitoric if it has only non-degenerate singularities, without hyperbolic blocks, and one of the components of generates a circle action. Semitoric systems have been...

Dustin Connery-Grigg (Université de Montreal), Geometry and topology of Hamiltonian Floer complexes in low-dimension

In this talk, I will present two results relating the qualitative dynamics of non-degenerate Hamiltonian isotopies on surfaces to...

In this talk I will discuss a joint project with Yuanpu Liang in which we establish several properties of the sequence of symplectic capacities defined by Gutt and Hutchings for star-shaped domains using $S^1$-equivariant symplectic homology. Among...

I will start by explaining the construction of a formal scheme starting with an integral affine manifold $Q$ equipped with a decomposition into Delzant polytopes. This is a weaker and more elementary version of degenerations of abelian varieties...

In this talk I will introduce barcode entropy and discuss its connections to topological entropy. The barcode entropy is a Floer-theoretic invariant of a compactly supported Hamiltonian diffeomorphism, measuring, roughly speaking, the exponential...

In a work with Jacques Fejoz, we consider the conformal dynamics on a symplectic manifold , i.e. for which the symplectic form is transformed colinearly to itself. In the non-symplectic case, we study the problem of isotropy and uniqueness of...

I will review two combinatorial constructions of integrable systems: Goncharov-Kenyon construction based on counting perfect matchings in bipartite graphs, and Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on counting paths in networks...

Benoît Joly (Ruhr-Universität Bochum), Barcodes for Hamiltonian homeomorphisms of surfaces

In this talk, we will study the Floer Homology barcodes from a dynamical point of view. Our motivation comes from recent results in symplectic topology using...

I will present two constructions of Kähler manifolds, endowed with Hamiltonian torus actions of infinite dimension. In the first example, zeroes of the moment map are related to isotropic maps from a surfaces in $\mathbb{R}^{2n}$. In the second...

The existence of rational plane curves of a given degree with prescribed singularities is a subtle and active area in algebraic geometry. This problem turns out to be closely related to difficult enumerative problems which arise in symplectic field...

The Hochschild cohomology of the Floer algebra of a Lagrangian $L$, and the associated closed-open string map, play an important role in the generation criterion for the Fukaya category and in deformation theory approaches to mirror symmetry. I will...

Let $K$ be a knot or link in the 3-sphere, thought of as the ideal boundary of hyperbolic 4-space, $H^{4}$. The main theme of my talk is that it should be possible to count minimal surfaces in $H^{4}$ which fill $K$ and obtain a link invariant. In...

In this talk, I want to show that in the planar circular restricted three body problem there are infinitely many symmetric consecutive collision orbits for all energies below the first critical energy value.  By using the Levi-Civita regularization...

To an element in the completion of the set of Lagrangians for the spectral distance we associate a support.  We show that such a support is γ-coisotropic (a notion we shall define in the talk) and we shall give examples and counterexamples of γ...

Daniel Rudolf (Ruhr-Universität Bochum): Viterbo‘s conjecture for Lagrangian products in $\mathbb{R}^4$

We show that Viterbo‘s conjecture (for the EHZ-capacity) for convex Lagrangian products in $\mathbb{R}^4$ holds for all Lagrangian products (any...

Gromov-Witten invariants for a general target are rational-valued but not necessarily integer-valued. This is due to the contribution of curves with nontrivial automorphism groups. In 1997 Fukaya and Ono proposed a new method in symplectic geometry...

Relative symplectic cohomology is a Floer theoretic invariant associated with compact subsets K of a closed or geometrically bounded symplectic manifold M. The motivation for studying it is that it is often possible to reduce the study of global...

I will explain how to construct the Ruelle invariant of a symplectic cocycle over an arbitrary measure preserving flow. I will provide examples and computations in the case of Hamiltonian flows and Reeb flows (in particular, for toric domains). As...

I will introduce a new version of symplectic homology that resembles the relative symplectic homology and that is related to the symplectic homology of a Liouville sector. This version, called selective symplectic homology, is associated with a...

What is the symplectic analogue of being convex? We shall present different ideas to approach this question. Along the way, we shall present recent joint results with J.Dardennes and J.Zhang on monotone toric domains non-symplectomorphic to convex...

Pierre-Alexandre Mailhot (Université de Montréal): The Spectral Diameter of a Liouville Domains and its Applications

The spectral norm provides a lower bound to the Hofer norm. It is thus natural to ask whether the diameter of the spectral norm is...

 We introduce new invariants to the existence of Lagrangian cobordisms in R^4. These are obtained by studying holomorphic disks with corners on Lagrangian tangles, which are Lagrangian cobordisms with flat, immersed boundaries.

We develop...

We present recent developments in symplectic geometry and explain how they motivated new results in the study of cluster algebras. First, we introduce a geometric problem: the study of Lagrangian surfaces in the standard symplectic 4-ball bounding...

Yash Deshmukh (Columbia University): Moduli Spaces of Nodal Curves from Homotopical Algebra

I will discuss how the Deligne-Mumford compactification of curves arises from the uncompactified moduli spaces of curves as a result of some algebraic...

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...