Seminars Sorted by Series

Machine learning algorithms are ubiquitous in most scientific, industrial and personal domains, with many successful applications. As a scientific field, machine learning has always been characterized by the constant exchanges between theory and...

Embedded contact homology gives a sequence of obstructions to four-dimensional symplectic embeddings, called ECH capacities. These obstructions are known to be sharp in several interesting cases, for example for symplectic embeddings of one...

ECH (embedded contact homology) capacities give obstructions to symplectically embedding one four-dimensional symplectic manifold with boundary into another. These obstructions are known to be sharp when the domain is a "concave toric domain" and...

We will discuss some recent constructions of "exotic" Lagrangian tori in simple symplectic manifolds such as $\mathbb{CP}^2$ (work of Renato Vianna) and $\mathbb R^6$ that are not Hamiltonian isotopic to previously known examples, inspired by wall...

We study symplectic invariants of the open symplectic manifolds $X$ obtained by plumbing cotangent bundles of spheres according to a plumbing tree. We prove that certain models for the Fukaya category $\mathcal F(X)$ of closed exact Lagrangians in...

I will describe how the notion of Lagrangian cobordism, introduced by Arnold in 1980, offers a systematic perspective on the study of Lagrangian topology. There are three aspects that will be emphasized: the relations with the triangulated structure...

We produce examples of non-trivial Hamiltonian fibrations that are not detected by previous methods (the characteristic classes of Reznikov for example), and improve theorems of Reznikov and Spacil on cohomology-surjectivity to the level of...

A point $q$ in a contact manifold $(M,\xi)$ is said to be a translated point of a contactomorphism $\phi$, with respect to a contact form $\alpha$ for $\xi$, if it is a "fixed point modulo the Reeb flow", i.e. if $q$ and $\phi(q)$ are in the same...

The Fukaya category of a Landau-Ginzburg (LG) model $W: E \to C$, denoted $F(E,W)$, enlarges the Fukaya category of $E$ to include certain non-compact Lagrangians determined by $W$ (for instance, Lefschetz fibrations and their thimbles). I will...

The log canonical threshold of a hypersurface singularity is an important invariant which appears in many areas of algebraic geometry. For instance it is used in the minimal model program, has been used to prove vanishing theorems, find Kahler...

We will describe how to get almost toric fibrations for all del Pezzo surfaces (endowed with monotone symplectic form), in particular for $\\mathbb{CP}^2\\#k\\overline{\\mathbb{CP}}^2$ for $4\\le k \\le 8$, where there is no toric fibrations. From...

There is growing interest in looking at operations on quantum cohomology that take into account symmetries in the holomorphic spheres (such as the quantum Steenrod powers, using a Z/p-symmetry). In order to prove relations between them, one needs to...

Given a smooth knot K in the 3-sphere, a classic question in knot theory is: What surfaces in the 4-ball have boundary equal to K? One can also consider immersed surfaces and ask a “geography” question: What combinations of genus and double points...

A central question from systolic geometry is to find upper bounds for the systolic ratio of a Riemannian metric on a closed $n$-dimensional manifold, i.e. the ratio of the $n$-th power of the shortest length of closed geodesics by the volume...

In this talk, I will address a geometric inverse problem from contact geometry: is it possible to recognize whether all orbits of a given Reeb flow are closed from the knowledge of the action spectrum? Borrowing the terminology from Riemannian...

This talk beings with a light introduction, including some historical anecdotes to motivate the development of this Floer theoretic machinery for contact manifolds some 25 years ago. I will discuss joint work with Hutchings which constructs...

Homological mirror symmetry predicts that the derived category of coherent sheaves on a curve has a symplectic counterpart as the Fukaya category of a mirror space. However, with the exception of elliptic curves, this mirror is usually a symplectic...

I will explain a duality theorem with products in Rabinowitz-Floer homology. This has a bearing on string topology and explains a number of dualities that have been observed in that setting. Joint work in progress with Kai Cieliebak and Nancy...

Morgan Weiler, Rice University:Infinite staircases of symplectic embeddings of ellipsoids into Hirzebruch surfaces

Gromov nonsqueezing tells us that symplectic embeddings are governed by more complex obstructions than volume. In particular, in...

Let f be a polynomial over the complex numbers with an isolated singular point at the origin and let d be a positive integer. To such a polynomial we can assign a variety called the dth contact locus of f. Morally, this corresponds to the space of d...

An exotic symplectomorphism is a symplectomorphism that is not isotopic to the identity through compactly supported symplectomorphisms.Using Floer-theoretic methods, we prove that the non-existence of an exotic symplectomorphism on the standard...

We present techniques for constructing families of compact, monotone (including exact) Lagrangians in certain affine varieties, starting with Brieskorn-Pham hypersurfaces. We will focus on dimensions 2 and 3. In particular, we'll explain how to set...

A classic result, due to McDuff and Schlenk, asserts that the function that encodes when a four-dimensional symplectic ellipsoid can be embedded into a four-dimensional ball has a remarkable structure: the function has infinitely many corners...

Knot Floer homology is an invariant for knots in three-space, defined as a Lagrangian Floer homology in a symmetric product. It has the form of a bigraded vector space, encoding topological information about the knot. I will discuss an algebraic...

Yusuke Kawamoto: Homogeneous quasimorphism, C^0-topology and Lagrangian intersection

Abstract: We construct an example of a non-trivial homogeneous quasimorphism on the group of Hamiltonian diffeomorphisms of the $2$- and $4$-dimensional quadric...

The classical Pontryagin–Thom isomorphism equates manifold bordism groups with corresponding stable homotopy groups. This construction moreover generalizes to the equivariant context. I will discuss work which establishes a Pontryagin--Thom...

In a joint work with Laurent Côté we show the following result. Any Lagrangian plane in the cotangent bundle of an open Riemann surface which coincides with a cotangent fibre outside of some compact subset, is compactly supported Hamiltonian...

In a joint work with Pierre Dehornoy and Ana Rechtman, we prove that on a closed 3-manifold, every nondegenerate Reeb vector field is supported by a broken book decomposition. From this property, we deduce that in dimension 3 every nondegenerate...

For a weighted homogeneous polynomial and a choice of a diagonal symmetry group, we define a new Fukaya category based on wrapped Fukaya category of its Milnor fiber together with monodromy information. It is analogous to the variation operator in...

This talk will discuss a new algebraic structure called triangulated persistence category (TPC). It combines the triangulated category structure with the persistence module structure. This algebraic structure can be used to associate a metric...

This talk reports on joint work with Maria Bertozzi, Tara Holm, Emily Maw, Grace Mwakyoma, Ana Rita Pires, and Morgan Weiler on a WiSCon project to investigate the embedding capacity function of the one-point blow up of $\mathbb CP^2$. We found...

The Arnold conjecture about fixed points of Hamiltonian diffeomorphisms was partly motivated by the celebrated Poincare-Birkhoff fixed point theorem for an area-preserving homeomorphism of an annulus in the plane. Despite the fact that the Arnold...

I will start by explaining Takahashi's homological mirror symmetry (HMS) conjecture regarding invertible polynomials, which is an open string reinterpretation of Berglund-Hubsch-Henningson mirror symmetry. In joint work with A. Polishchuk, we...

Viterbo conjectured that a normalized symplectic capacity, on convex domains of a given volume, is maximized for the ball. A stronger version of this conjecture asserts that all normalized symplectic capacities agree on convex domains. Since...

Simon Allais (ENS Lyon)

Title: Generating functions in Hamiltonian dynamics and symplectic-contact rigidity

Abstract: Generating functions of Hamiltonian diffeomorphisms are maps that can be seen as finite dimensional versions of the action...

This talk is about joint work with Nancy Hingston and Alexandru Oancea. We describe various secondary coproducts on the Floer homology of a cotangent bundle and show that, under Viterbo's isomorphism, they all correspond to the Goresky-Hingston...

Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The...

Triangulated categories play an important role in symplectic topology. The aim of this talk is to explain how to combine triangulated structures with persistence module theory in a geometrically meaningful way. The guiding principle comes from the...

Yu-Wei Fan (Berkeley),Shifting numbers in triangulated categories
 
Abstract: One can consider endofunctors of triangulated categories as categorical dynamical systems, and study their long term behaviors under large iterations. There are (at least...

In this talk, I will address the (singular) Weinstein conjecture about the existence of (singular) periodic orbits of Reeb vector fields on compact manifolds endowed with singular contact forms. Our motivating examples come from Celestial mechanics...

I will explain the construction of a functor from the exact symplectic cobordism category to a totally ordered set, which measures the complexity of the contact structure. Those invariants are derived from a bi-Lie infinity formalism of the rational...