Seminars Sorted by Series

We will ask how many Lagrangian tori, say with an integral area class, can be `packed' into a given symplectic manifold. Similarly, given an arrangement of such tori, like the integral product tori in Euclidean space, one can ask about the...

The $C^0$ flux conjecture predicts that a symplectic diffeomorphism that can be $C^0$ approximated by a Hamiltonian diffeomorphism is itself Hamiltonian. We describe how the flux conjecture relates to new instances of the strong Arnol’d conjecture...

Chaidez and Edtmair have recently found the first examples of dynamically convex domains in $R^4$ that are not symplectomorphic to convex domains (called symplectically convex domains), answering a long-standing open question. In this talk we shall...

An old problem in classical mechanics is the existence of periodic flows within specific classes of Hamiltonian systems such as geodesic and magnetic flows, and central forces. In the last years, interest in this problem has been revitalized since...

A compact invariant set of a flow is called locally maximal when it is the largest invariant set in some neighborhood. In this talk, based on joint work with Erman Cineli, Viktor Ginzburg, and Basak Gurel, I will present a "forced existence" result...

An old open question in symplectic geometry asks whether all normalised symplectic capacities coincide for convex domains in the standard symplectic vector space. I will show that this question has a positive answer for smooth convex domains which...

Results concerning rigidity of Lagrangian submanifolds lie at the heart of symplectic topology, and have been intensively studied since the 1990s. An example for this phenomenon is the concept of Lagrangian Barriers, a form of symplectic rigidity...

In the study of Hamiltonian systems, integrable dynamics play a crucial role. Integrability, however, appears to be a delicate property that is not expected to persist under generic small perturbations. Understanding the essence of this fragility...

The dynamics associated with mechanical Hamiltonian flows with smooth potentials that include sharp fronts may be modeled, at the singular limit, by Hamiltonian impact systems: a class of generalized billiards by which the dynamics in the domain’s...

I'll explain joint work in progress with Abbondandolo and Kang concerning the Clarke dual action functional of convex domains and pseudoholomorphic planes. In dimension 4, I'll explain applications to the knot types of periodic Reeb orbits.

In the late '90s, Eliashberg and Thurston established a remarkable connection between foliations and contact structures in dimension three: any co-oriented, aspherical foliation on a closed, oriented 3-manifold can be approximated by positive and...

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...

I will give a construction of certain Q-valued deformation invariants of (in particular) complete non-positively curved Riemannian manifolds. These are obtained as certain elliptic Gromov-Witten curve counts. As one immediate application we give the...

In their 2001 paper, Hofer, Wysocki and Zehnder conjectured that every autonomous Hamiltonian flow has either two or infinitely many simple periodic orbits on any compact star-shaped energy level; in the same paper, the authors prove this assuming...

In joint work with Bulent Tosun, it was shown that Heegaard Floer theory provides an obstruction for a contact 3-manifold to embed as a contact type hypersurface in standard symplectic 4-space. As one consequence, no Brieskorn homology sphere admits...

Legendrian Contact Homology (LCH) was among the first, and is still among the most important, non-classical invariants of Legendrian knots. In this talk, I will tell a story that builds up ever more sophisticated analogues of Poincare Duality in LCH...

We discuss the shape invariant, a sort of set valued symplectic capacity defined by the Lagrangian tori inside a domain of $R^4$. Partial computations for convex toric domains are sometimes enough to give sharp obstructions to symplectic embeddings...

For the past 25 years, a key player in contact topology has been the Floer-theoretic invariant called Legendrian contact homology. I'll discuss a package of new invariants for Legendrian knots and links that builds on Legendrian contact homology and...

Since the beginning of the subject, it has been speculated that Gromov-Witten invariants should admit refinements in complex cobordism. I will propose a resolution of this question based on joint work-in-progress with Abouzaid, building on recent...

I will discuss an adaptation of Gromov's ideal-valued measures to symplectic topology. It leads to a unified viewpoint at three "big fiber theorems": the Centerpoint Theorem in combinatorial geometry, the Maximal Fiber Inequality in topology, and...

I will discuss a recent proof of new cases of the Hilbert-Smith conjecture for actions by homeomorphisms of symplectic nature. In particular, it rules out faithful actions of the additive $p$-adic group in this setting and provides further...

Relative symplectic cohomology, an invariant of subsets in a symplectic manifold, was recently introduced by Varolgunes. In this talk, I will present a generalization of this invariant to pairs of subsets, which shares similar properties with the...

In 1987, Hofer and Zehnder showed that for any smooth function $H$ on $\mathbb{R}^{2n}$, almost every compact and regular level set contains at least one closed characteristic. I'll show that, when $n = 2$, almost every compact and regular level set...

Algebraic torsion is a means of understanding the topological complexity of certain homomorphic curves counted in some Floer theories of contact manifolds.  This talk focuses on algebraic torsion and the contact invariant in embedded contact...

I will introduce a new structure on (relative) Symplectic Cohomology defined in terms of a PROP called the “Plumber’s PROP.” This PROP consists of nodal Riemann surfaces, of all genera and with multiple inputs and outputs, satisfying a condition...

Symplectic manifolds exhibit curious behaviour at the interface of rigidity and flexibility. A non-squeezing phenomenon discovered by Gromov in the 1980s was the first manifestation of this. Since then, extensive research has been carried out into...

By the Birkhoff Ergodic Theorem, the asymptotic mean action of an area-preserving map is defined almost everywhere. Bramham and Zhang asked whether, if a map is a pseudo-rotation, its asymptotic mean action is defined everywhere and is constant. In...

I will explain the relationship between the cyclotomic structure on symplectic cohomology and the equivariant pants products. This relationship exists for any cohomology theory (in particular, I will give a definition of the equivariant pants...

Distinct Hamiltonian isotopy classes of monotone Lagrangian tori in $\mathbb{C} P^2$ can be associated to Markov triples. With two exceptions, each of these tori are symplectomorphic to exactly three Hamiltonian isotopy classes of tori in the ball...

Apart from the usual transversality problems in defining curve counting invariants, when defining the open Gromov-Witten invariants of a Lagrangian one has to deal with the fact that the moduli spaces have boundary. Thus a homological (virtual)...

I will discuss the occurrence of some notions and results from contact topology in the context of equilibrium and non-equilibrium thermodynamics. Based on joint works with Michael Entov and Lenya Ryzhik.

Consider a contact three-manifold, and within it a symplectic surface with boundary on Reeb orbits. We show that assuming a certain inequality on the rotation numbers of the boundary Reeb orbits, there must exist Reeb orbits which intersect the...

The growth of an autonomous Hamiltonian flow in Hofer's metric is not yet well understood. A result of Polterovich and Rosen shows that generically this growth is asymptotically linear, and in all known cases where it is not, it appears to be...

Let Y be a symplectic divisor of X, $\omega$. In the Kahler setting, Givental's Quantum Lefschetz formula relates certain Gromov-Witten invariants (encoded by the G function) of X and Y. Given an Lagrangian L in (Y, $\omega$|Y), we can lift it to a...

The spectral norm on the group of Hamiltonian diffeomorphisms of a symplectic manifold is defined via a homological min-max process on the filtered Floer homology. Based on the spectral norm one defines the spectral capacity of domains which is...

We show that skein valued counts of open holomorphic curves in a symplectic Calabi-Yau 3-fold with Maslov zero Lagrangian boundary condition are invariant under deformations and discuss applications (Ooguri-Vafa conjecture and simple recursion...

We will explore certain $C^0$-rigidity and flexibility phenomena in the study of contact transformations. In particular, we will show how the dichotomy between contact squeezing and non-squeezing is reflected in the group of contact homeomorphisms...

In a series of papers with Alexander Ritter, we construct a symplectic cohomology for open non-convex symplectic manifolds that admit pseudo-holomorphic C*-actions. Out of this construction, we get a filtration on ordinary cohomology of these...

The open Gromov-Witten (OGW) potential is a function defined  on the Maurer-Cartan space of a closed Lagrangian submanifold in a  symplectic manifold with values in the Novikov ring. From the values  of the OGW potential, one can extract so-called...

(joint work with Shaoyun Bai) Using a new version of transversality condition (the FOP transversality) on orbifolds, one can construct Hamiltonian Floer theory over integers for all compact symplectic manifolds. In this talk I will first describe...

A hypersurface in a contact manifold is convex if there is a contact vector field that is transverse to it. Convex surfaces have long been a fundamental tool in 3-dimensional contact topology. In higher dimensions, convex hypersurfaces remained...

In this talk we discuss a relation between the contact version 
of the Hofer norm and positive loops of contactomorphisms.
This leads to a new criterion for the existence of contractible positive 
loops in terms of open book decompositions and...

In this talk, we will present a proof of contact big fiber theorem, based on invariants read off from contact Hamiltonian Floer homology. The theorem concludes that any contact involutive map on a Liouville fillable contact manifold admits at least...

This talk is based on joint work with Yang Li. I will discuss the problem of counting special Lagrangians in Calabi-Yau 3-folds and Fueter sections to define new numerical and Floer-theoretic invariants. The key challenges are the non-compactness...

In this talk I will explain some quantitative embedding results for Legendrian submanifolds of pre-quantization spaces. To start, I will recall some contact non-squeezing results for domains, and present an elementary proof of Legendrian non...

Given a Morse function on a closed smooth manifold and a Smale gradient-like vector field adapted to it, one can construct a topological category called the flow category associated with this data. Its objects are the critical points of the function...

The purpose of the talk is to discuss a class of pseudo-metrics that can be defined on the set of objects of a triangulated category whose morphisms are endowed with a notion of weight. In case the objects are Lagrangian submanifolds (possibly...

I will explain recent joint work proving that the group of compactly supported area preserving homeomorphisms of the two-disc is not a simple group; this answers the ”Simplicity Conjecture” in the affirmative. Our proof uses new spectral invariants...

Compatible almost-complex structures on symplectic manifolds correspond to optimal quantizations. I will discuss this statement (joint with Louis Ioos and David Kazhdan), as well as some other geometric facets of uncertainty principles in quantum...