Seminars Sorted by Series

Many Floer-type theories are the categorifications of classical invariants. We describe a program of classification of such theories: we consider them as local systems on the spaces of manifolds that we constructed and extend them to the singular...

I will describe a system of differential equations for the genus 0 open Gromov-Witten potential of a Lagrangian submanifold fixed by an anti-symplectic involution. These equations involve both the open Gromov-Witten potential and the closed Gromov...

Conventional Riemann-Hilbert correspondence relates the category of holonomic $D$-modules (de Rham side) with the category of constructible sheaves (Betti side). I am going to reconsider this relationship from the point of view of deformation...

Abstract: It is believed that topologically ordered gapped local Hamiltonians in 2+1d consisting of commuting terms may not realize a chiral anyon theory. There is even a formula that expresses the chiral central charge of the edge theory as an...

We will present two results in complex geometry: (1) A Kähler compactification of $\mathbb{C}^n$ with a smooth divisor complement must be $\mathbb{P}^n$, which confirms a conjecture of Brenton and Morrow under the Kähler assumption; (2) Any complete...

We will outline the proof of an intersection result between embedded Lagrangian tori and certain 1 parameter families of product Lagrangian tori in the 4 dimensional symplectic cylinder. The theorem can be applied to give new computations of the...

I will describe and argue the existence of contact non-squeezing phenomena in contact lens spaces and in strongly orderable prequantizations.
The proof is based on the construction of contact capacities coming from spectral selectors defined on the...

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 related to the Rokhlin property of the group of...

The talk will be on recent progress in a series of joint papers with Filip Živanović, about a large class of non-compact symplectic manifolds, which includes semiprojective toric manifolds, quiver varieties, and conical symplectic resolutions of...

The parametrised Whitehead torsion is an invariant of families of manifolds, and can be viewed as a map to an algebraic K-theory space. A strong version of the nearby Lagrangian conjecture says that when applied to families of closed exact...

The double bubble plumbing, first studied by Smith and Wemyss, is a Stein neighborhood of two Lagrangian 3-spheres intersecting cleanly along an unknotted circle in some 6-dimensional symplectic manifold. Depending on the identification of the...

In this talk, we will explore the relationship between the geometry and topology of a complexity-one four-manifold and the combinatorial data that encode it. We will use a generators-and-relations description for the even part of the equivariant...

It is well-known that the geodesic flow on ellipsoids of revolution is integrable. In joint work with Ferreira and Vicente, we used this fact to obtain a symplectomorphism between the unit disk bundle of such an ellipsoid without fiber and a toric...

Given a Lagrangian L, I will discuss the existence of a neighborhood W of L with the following property: for any Hamiltonian diffeomorphism f, if f(L) is contained inside W, then f(L) intersects L. On the one hand, for any symplectic manifold of...

The talk will be on recent progress in a series of joint papers with Filip Živanović, about a large class of non-compact symplectic manifolds, which includes semiprojective toric manifolds, quiver varieties, and conical symplectic resolutions of...

One can associate an HDHF (symmetric) wrapped Fukaya category to a Liouville domain by counting higher genus curves, which are required to be branched covers. For the cotangent bundle of an orientable surface with genus at least one Honda, Tian, and...

In this talk, we will discuss new infinite symplectic staircases. Much recent progress has been made in the study of infinite symplectic staircases arising from embedding problems of standard ellipsoids into various symplectic four-manifolds. We...

In this talk we discuss the multiplicity question for prime closed orbits of a dynamically convex Reeb flow on the boundary of a $2n$-dimensional star-shaped domain. Our first main result asserts that such a flow has at least n prime closed Reeb...

Shuo Zhang (Morningside Center of Mathematics):Composed Dehn twist exact sequence through quilts and $(A_\infty,n)$ modules

We prove the quilted Floer cochain complexes form $(A_\infty,n)$ modules over the Fukaya category $Fuk(M \times M^-)$. Then...

We consider a class of Lagrangian sections L contained in certain Calabi-Yau Lagrangian fibrations (mirrors of toric weak Fano manifolds). We prove that a form of the Thomas-Yau conjecture holds in this case: L is Hamiltonian isotopic to a special...

Consider a symplectic surface in a three-dimensional contact manifold with boundary on Reeb orbits. We assume that the rotation numbers of the boundary Reeb orbits satisfy a certain inequality, and we also make a technical assumption that the Reeb...

The chord conjecture, due initially to Arnol'd in the case of the standard contact three-sphere, asserts the existence of a Reeb chord with boundary on every closed Legendrian submanifold of a closed contact manifold for every contact form. This...

Baptiste Serraille (ETH Zürich)On a Linear Combination of Link Spectral Invariants on the Sphere:

Link spectral invariants and their homogenizations have been defined by Cristofaro-Gardiner et.al. In joint work with Ibrahim Trifa, we define a linear...

The symplectic area of a Lagrangian submanifold L in a symplectic manifold is defined as the minimal positive symplectic area of a smooth 2-disk with boundary on L. A Lagrangian torus is called extremal if it maximizes the symplectic area among all...

The Birkhoff attractor is a closed invariant subset associated with any dissipative twist map of the annulus (of dimension 2), which was introduced by Birkhoff in 1932. We will see that it can be generalized to higher dimensions using tools from...

Julio Sampietro Christ  (Université Paris-Saclay) : Equivariant Lagrangian Non-Displacements

Lagrangian Floer theory is useful to detect non-displaceability of Lagrangian submanifolds via Hamiltonian isotopies. A related question, in the presence of...

A convex toric domain $X_\Omega$ is a 4-dimensional subset of $\mathbb{R}^4$, defined as the preimage of a bounded convex region $\Omega$ in the positive quadrant of $\mathbb{R}^2$ under the moment map. We consider how geometric features of $\Omega$...

I will begin by motivating the study of invariant distances on spaces of Legendrians. I will then discuss two main results:
(a) the construction of a new unbounded invariant distance on the universal cover of many Legendrian isotopy classes ;
(b) the...

Helicity is an invariant of divergence free vector fields on a three-manifold. One of its fundamental properties is invariance under volume preserving diffeomorphisms. Arnold, having derived an ergodic interpretation of helicity as an asymptotic...

Levin Maier (Heidelberg University) : From Geometric Hydrodynamics to Periodic Geodesics on Manifolds of Mappings

In this talk, we begin by recalling Arnold’s geometric formulation of hydrodynamics and then extend this framework to a broader class of...

Locally conformally symplectic (LCS) manifolds are generalisations of symplectic manifolds where the 2-form is not closed but instead satisfies the identity dω = η ∧ ω for a closed 1-form η. The study of these manifolds is equivalent to that of...

The group of Hamiltonian diffeomorphisms , equipped with the Hofer metric , is a central object in symplectic topology. A landmark result by Polterovich and Shelukhin established the profound geometric complexity of this group for surfaces and their...

This talk, which is based on two joint works, one with Pedro Salomão and Richard Siefring and another with Michael Hutchings and Vinicius Ramos, revolves around the role that restrictions on the knot types of periodic Reeb orbits imposed by the...

Emilia Konrad (Augsburg University) :Construction of Constrained Floer Homology

We consider the symplectic area functional, constrained to loops of vanishing Hamiltonian mean value: It has the same critical points as the Rabinowitz action functional...