Seminars Sorted by Series

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...

ICM 2022 will be held virtually this year.  Please join Camillo De Lellis, Ronen Eldan, and Avi Wigderson as they give live presentations of their ICM lectures.  The schedule and abstracts are as follows:

• 1:00 PM - Camillo De Lellis, IAS
• 2:00 PM...

Thin groups are finitely generated, infinite index subgroups of arithmetic lattices in Lie groups. Interesting examples come from monodromies of families of algebraic manifolds and in these cases, the "thinness" of monodromy is explained by special...

In his study of the Baum-Connes conjecture, Vincent Lafforgue was lead to study Banach space representations of SL(n>2,F) (for F a local field) which are not by isometries but by operators of slowly growing norm. Classical tools to study unitary...

The classical Lagrange and Markov spectra encode the features of certain Diophantine approximations problems. The first systematic study of these spectra was done by Markov in 1880. Since then, these objects attracted the attention of several...

The purpose of the talk is to explain how additive combinatorics plays a role in recent work on the dimension of self-affine measures generated by maps satisfying a diophantine condition. Under low-entropy or separation assumptions, this problem is...

We show that closed negatively curved locally symmetric spaces are characterized among nearby Riemannian manifolds by the Lyapunov exponents of their geodesic flow along periodic orbits. Our methods extend to locally characterize the geodesic flows...

This talk will give a detailed introduction to the proof of Zimmer's conjecture made in recent work with Brown and Hurtado. The talk will be independent of Monday's member seminar, but I will not repeat history and motivation. I will begin by (re...

Ratner's celebrated equidistribution theorem states that the trajectory of any point in a homogeneous space under a unipotent flow is getting equidistributed with respect to some algebraic measure. In the case where the action is horospherical, one...

The "linearization" technique is a powerful method in homogeneous dynamics to control the time a unipotent orbit spends in the vicinity of a closed homogeneous subset. This method relies on the polynomial nature of a unipotent flow and does not...

Let $X \subset \R^N$ be a Borel set, $\mu$ a Borel probability measure on $X$ and $T:X \to X$ a Lipschitz and injective map. Fix $k \in \N$ greater than the (Hausdorff) dimension of $X$ and assume that the set of $p$-periodic points has dimension...

We will discuss results connecting the titular objects on infinite graphs, including some known results by Varopoulos and Coulhon and Saloff-Coste and some new resutls.

I'll try to explain what we currently understand about the theoretical power of quantum computers, in a way that's accessible to a general math and physics audience. In particular, I'll demolish the popularly-held belief that quantum computing means...