Seminars Sorted by Series

The talk will focus on the question of whether existing symplectic methods can distinguish pseudo-rotations from rotations (i.e., elements of Hamiltonian circle actions). For the projective plane, in many instances, but not always, the answer is...

Alexandre Jannaud (Sorbonne),Dehn-Seidel twist, $C^0$ symplectic geometry and barcodes
Abstract: In this talk I will present my work initiating the study of the $C^0$ symplectic mapping class group, i.e. the group of isotopy classes of symplectic...

The purpose of this talk is to explore how Lagrangian Floer homology groups change under (non-Hamiltonian) symplectic isotopies on a (negatively) monotone symplectic manifold $(M,\omega)$ satisfying a strong non-degeneracy condition. More precisely...

One of the earliest fundamental applications of Lagrangian Floer theory is detecting the non-displaceablity of a Lagrangian submanifold. Many progress and generalisations have been made since then but little is known when the Lagrangian submanifold...

Gross and Siebert have recently proposed an "intrinsic" programme for studying mirror symmetry. In this talk, we will discuss a symplectic interpretation of some of their ideas in the setting of affine log Calabi-Yau varieties. Namely, we describe...

I will explain the notion of twisted generating function and show that a closed exact Lagrangian submanifold $L$ in the cotangent bundle of $M$ admits such a thing. The type of function arising in our construction is related to Waldhausen's tube...

The group of Hamiltonian diffeomorphisms of a symplectic manifold admits a remarkable bi-invariant metric, called Hofer’s metric. My talk will be about a recent joint work with Dan Cristofaro-Gardiner and Vincent Humilière resolving the following...

A classical construction in topology associates to a space $X$ and prime $p$, a new "localized" space $X_p$ whose homotopy and homology groups are obtained from those of $X$ by inverting $p$. In this talk, I will discuss a symplectic analog of this...

We study configurations of disjoint Lagrangian submanifolds in certain low-dimensional symplectic manifolds from the perspective of the geometry of Hamiltonian maps. We detect infinite-dimensional flats in the Hamiltonian group of the two-sphere...

Jesse Huang (UIUC), Variation of FLTZ skeleta

In this short talk, I will discuss an interpolation of FLTZ skeleta mirror to derived equivalent toric varieties. This is joint work with Peng Zhou.

Shaoyun Bai (Princeton), $SU(n)$–Casson invariants...

In all known explicit computations on Weinstein manifolds, the self-wrapped Floer homology of non-compact exact Lagrangian is always either infinite-dimensional or zero. We will explain why a global variant of this observed phenomenon holds in broad...

We define a quantum product on the cohomology of a symplectic manifold relative to a Lagrangian submanifold, with coefficients in a Novikov ring. The associativity of this product is equivalent to an open version of the WDVV equations for an...

Maxim Jeffs (Harvard), Mirror symmetry and Fukaya categories of singular varieties

In this talk I will explain Auroux' definition of the Fukaya category of a singular hypersurface and two results about this definition, illustrated with some...

I will discuss joint work with Olga Plamenevskaya studying symplectic fillings of links of certain complex surface singularities, and comparing symplectic fillings with complex smoothings. We develop characterizations of the symplectic fillings...

The h-principle for the simplification of caustics (i.e. Lagrangian tangencies) reduces a geometric problem to a homotopical problem. In this talk I will explain the solution to this homotopical problem in the case of spheres. More precisely, I will...

Oğuz Şavk (Boğaziçi University), Classical and new plumbings bounding contractible manifolds and homology balls

A central problem in low-dimensional topology asks which homology 3-spheres bound contractible 4-manifolds and homology 4-balls. In this...

K3 surfaces have a rich geometry and admit interesting holomorphic automorphisms. As examples of Calabi-Yau manifolds, they admit Ricci-flat Kähler metrics, and a lot of attention has been devoted to how these metrics degenerate as the Kähler class...

In his search for closed orbits in the planar restricted three-body problem, Poincaré’s approach roughly reduces to:

1. Finding a global surface of section;
2. Proving a fixed-point theorem for the resulting return map.

This is the setting for the...

Mohan Swaminathan (Princeton),Super-rigidity and bifurcations of embedded curves in Calabi-Yau 3-folds

I will describe my recent work, joint with Shaoyun Bai, which studies a class of bifurcations of moduli spaces of embedded pseudo-holomorphic...

While by a result of McDuff the space of symplectic embeddings of a closed 4-ball into an open 4-ball is connected, the situation for embeddings of cubes $C^4 = D^2 \times D^2$ is very different. For instance, for the open ball $B^4$ of capacity 1...

There is notion of a smooth categorical compactification of dg/A-infinity categories: for example, a smooth compactification of algebraic varieties induces a smooth categorical compactification of the associated bounded dg categories of coherent...

An exceptionally gifted mathematician and an extremely complex person, Floer exhibited, as one friend put it, a "radical individuality." He viewed the world around him with a singularly critical way of thinking and a quintessential disregard for...

Title:Convergence and Riemannian bounds on Lagrangian submanifolds

Abstract: Recent years have seen the appearance of a plethora of possible metrics on spaces of Lagrangian submanifolds. Indeed, on top of the better...

In various areas of mathematics there exist "big fiber theorems", these are theorems of the following type: "For any map in a certain class, there exists a 'big' fiber", where the class of maps and the notion of size changes from case to case.

We...

This talk is based on a joint work with Thomas Kragh. Using the generating function theory we split inject homotopy groups of pseudo-isotopy and/or h-cobordism spaces into various spaces of Legendrian manifolds, e.g. the space of Legendrian unknots...

Rohil Prasad (Princeton), The smooth closing lemma for area-preserving surface diffeomorphisms

In this talk, I will discuss recent joint work with D. Cristofaro-Gardiner and B. Zhang showing that a generic area-preserving diffeomorphism of a closed...

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...