Seminars Sorted by Series

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...

I will present two constructions of Kähler manifolds, endowed with Hamiltonian torus actions of infinite dimension. In the first example, zeroes of the moment map are related to isotropic maps from a surfaces in $\mathbb{R}^{2n}$. In the second...

The existence of rational plane curves of a given degree with prescribed singularities is a subtle and active area in algebraic geometry. This problem turns out to be closely related to difficult enumerative problems which arise in symplectic field...

The Hochschild cohomology of the Floer algebra of a Lagrangian $L$, and the associated closed-open string map, play an important role in the generation criterion for the Fukaya category and in deformation theory approaches to mirror symmetry. I will...

Let $K$ be a knot or link in the 3-sphere, thought of as the ideal boundary of hyperbolic 4-space, $H^{4}$. The main theme of my talk is that it should be possible to count minimal surfaces in $H^{4}$ which fill $K$ and obtain a link invariant. In...

In this talk, I want to show that in the planar circular restricted three body problem there are infinitely many symmetric consecutive collision orbits for all energies below the first critical energy value.  By using the Levi-Civita regularization...

To an element in the completion of the set of Lagrangians for the spectral distance we associate a support.  We show that such a support is γ-coisotropic (a notion we shall define in the talk) and we shall give examples and counterexamples of γ...

Daniel Rudolf (Ruhr-Universität Bochum): Viterbo‘s conjecture for Lagrangian products in $\mathbb{R}^4$

We show that Viterbo‘s conjecture (for the EHZ-capacity) for convex Lagrangian products in $\mathbb{R}^4$ holds for all Lagrangian products (any...

Gromov-Witten invariants for a general target are rational-valued but not necessarily integer-valued. This is due to the contribution of curves with nontrivial automorphism groups. In 1997 Fukaya and Ono proposed a new method in symplectic geometry...

Relative symplectic cohomology is a Floer theoretic invariant associated with compact subsets K of a closed or geometrically bounded symplectic manifold M. The motivation for studying it is that it is often possible to reduce the study of global...