Seminars Sorted by Series

(This is a somewhat old-fashioned talk.) I will review the definition of symplectic cohomology and its deformation, for the complement of a smooth anticanonical divisor in a monotone symplectic manifold. The deformed group, with the parameter q...

While convex hypersurfaces are well understood in 3d contact topology, we are just starting to explore their basic properties in high dimensions. I will describe how to compute contact homologies (CH) of their neighborhoods, which can be used to...

Lukas Nakamura (University of Upsala):

A Metric on the Contactomorphism Group of an Orderable Contact Manifold: We discuss some properties of a pseudo-metric on the contactomorphism group of a strict contact manifold M induced by the maximum/minimum...

Spectral invariants defined via Embedded Contact Homology (ECH) or the closely related Periodic Floer Homology (PFH) satisfy a Weyl law: Asymptotically, they recover symplectic volume. This Weyl law has led to striking applications in dynamics...

Given a grid diagram for a knot or link in the three-sphere, we construct a spectrum whose homology is the knot Floer homology of . We conjecture that the homotopy type of the spectrum is an invariant of . Our construction does not use holomorphic...

The C0 distance on the space of contact forms on a contact manifold has been studied recently by different authors. It can be thought of as an analogue for Reeb flows of the Hofer metric on the space of Hamiltonian diffeomorphisms. In this talk, I...

• Julien Dardennes:The Coarse Distance from Dynamically Convex to Convex:

  Chaidez and Edtmair have recently found the first examples of dynamically convex domains in $R^4$ that are not symplectomorphic to convex domains, answering a long-standing open...

I will discuss how to build small symplectic caps for contact manifolds as a step in building small closed symplectic 4-manifolds. As an application of the construction, I will give explicit handlebody descriptions of symplectic embeddings of...

Floer homotopy type refines the Floer homology by associating a (stable) homotopy type to an Hamiltonian, whose homology gives the Hamiltonian Floer homology. In particular, one expects the existing structures on the latter to lift as well, such as...

• Francesco Morabito:Hofer Norms on Braid Groups and Quantitative Heegaard-Floer Homology

  Given a lagrangian link with k components it is possible to define an associated Hofer norm on the braid group with k strands. In this talk we are going to...

I will discuss a recursive formula for the homotopy type of the space of Legendrian embeddings of sufficiently positive cables with the maximal Thurston-Bennequin invariant. Via this formula, we identify infinitely many new components within the...

• Johanna Bimmermann :From Magnetically Twisted to Hyperkähler 

  The tangent bundle of a Kähler manifold admits in a neighborhood of the zero section a hyperkähler structure. From a symplectic point of view, this means we have three symplectic...

I will discuss the relationship between positive loops of contactomorphisms of a fillable contact manifold and the symplectic cohomology (SH) of the filling. The main result is that the existence of a positive loop which is "extensible" implies SH...

An old open question in symplectic topology is whether all normalized capacities coincide on convex bounded domains in the standard symplectic vector space. I will discuss this question for domains which are close to the Euclidean ball and its...

Given a Lagrangian torus fibration on the complement of an anticanonical divisor in a Kahler manifold, one usually constructs a mirror space by gluing local charts (moduli spaces of objects of the Fukaya category supported on generic torus fibers)...

Strong inversions are a class of order-2 symmetries of knots in . Building on work of Seidel-Smith, Lidman-Manolescu, Stoffregen-Zhang, and others, we will describe a relationship between the Khovanov homology of a knot with a strong inversion and...

I will discuss how much the choice of coefficients impacts the quantitative information of Floer theory, especially spectral invariants. In particular, I will present some phenomena that are specific to integer coefficients, including an answer to a...

Around twenty years ago Emmanuel Giroux formulated the equivalence of contact structures and open book decompositions with Weinstein pages up to stabilization. We establish the Giroux correspondence in full generality using the recent developments...

• Yao Xiao : Equivariant Lagrangian Floer Theory on Compact Toric Manifolds

  We introduce an equivariant Lagrangian Floer theory on compact symplectic toric manifolds. We define a spectral sequence to compute the equivariant Floer cohomology. We show...

• Yan-Lung Leon Li :Equivariant Lagrangian Correspondence and a Conjecture of Teleman

  It has been a continuing interest, often with profound importance, in understanding the geometric and topological relationship between a Hamiltonian G-manifold Y and...

An old question of Poincaré concerns creating periodic orbits via perturbations of a flow/diffeomorphism. While pseudoholomorphic methods have successfully addressed this question in dimensions 2-3, the higher-dimensional case remains less...

In this talk, we will consider a stabilized version of the fundamental existence problem of symplectic structures (cf. Open Problem 1 in McDuff & Salamon). Given a formal symplectic manifold, i.e. a closed manifold $M$ with a non-degenerate 2-form...

The presence of hyperbolic periodic orbits or invariant sets often has an affect on the global behavior of a dynamical system. In this talk we discuss two theorems along the lines of this phenomenon, extending some properties of Hamiltonian...

We discuss constraints on exact Lagrangian embeddings obtained from considering bordism classes of flow modules over Lagrangian Floer flow categories. This talk reports on joint work with Noah Porcelli.

For the past 25 years, Legendrian contact homology has played a key role in contact topology. I'll discuss a package of new invariants for Legendrian knots and links that builds on Legendrian contact homology and is derived from rational symplectic...

Toric integrable systems, also known as symplectic toric manifolds, arise as examples in different contexts within geometry and related areas. Semitoric integrable systems are a generalization of toric integrable systems in dimension four. In this...

It is conjectured that every Reeb flow on a closed three-manifold has either two, or infinitely many, simple periodic orbits. I will survey what is currently known about this conjecture. Then, I will try to explain some of the key ideas behind...

Chen and Ruan constructed symplectic orbifold Gromov-Witten invariants more than 20 years ago.  In ongoing work with Alex Ritter, we show that moduli spaces of pseudo-holomorphic curves mapping to a symplectic orbifold admit global Kuranishi charts...

Given a path-connected topological space X, a differential graded (DG) local system (or derived local system) is a module over the DGA of chains on the based loop space of X. I will explain how to define in the symplectically aspherical case...

Associated to a star-shaped domain in $\mathbb{R}^{2n}$ are two increasing sequences of capacities: the Ekeland-Hofer capacities and the so-called Gutt-Hutchings capacities. I shall recall both constructions and then present the main theorem that...

• Adrien Currier (Université de Nantes) :Exact Lagrangians in Cotangent Bundles with Locally Conformally Symplectic Structure

  First considered by Lee in the 40s, locally conformally symplectic (LCS) geometry appears as a generalization of symplectic...

We show that two generic, open, convex or concave toric domains in $R^4$ are symplectomorphic if and only if they agree up to reflection. The proof uses barcodes in positive $S^1$-equivariant symplectic homology, or equivalently in cylindrical...

• Sebastian Haney (Columbia University) :Open enumerative mirror symmetry for lines in the mirror quintic

  One of the earliest achievements of mirror symmetry was the prediction of genus zero Gromov-Witten invariants for the quintic threefold in terms...

Based on the exotic Lagrangian tori constructed in CP$^2$ by Vianna and Galkin-Mikhalkin, we construct for each Markov triple three monotone Lagrangian tori in the 4-ball, and for triples with distinct entries show that these tori lie in different...

Kaledin established a Cartier isomorphism for cyclic homology of dg-categories over fields of characteristic p, generalizing a classical construction in algebraic geometry. In joint work with Paul Seidel, we showed that this isomorphism and related...

In this talk I will first define the space of h-cobordisms associated to a manifold M. This space is known to have many non-trivial homotopy groups and in stable range (they can often be computed using Waldhausen's algebraic K-theory of spaces). I...

Jae Hee Lee (Stanford University) :Quantum Steenrod Operations, p-curvature, and Representation Theory

Quantum Steenrod operations are deformations of classical Steenrod operations on mod p cohomology defined by counts of genus 0 holomorphic curves...

Zhen Gao (Universität Augsburg) :Morse-Bott Floer Homology and Rectangular Pegs

The rectangular peg problem, an extension of the square peg problem, is easy to outline but challenging to prove through elementary methods. In this talk, I discuss how...

Alexia Corradini (University ofCambridge) :The Lagrangian Ceresa Cycle

In algebraic geometry, the Ceresa cycle provided one of the first examples of a nullhomologous cycle which is not algebraically trivial. I will explain how one can obtain a...

We will discuss a new construction of space-times in the title with $\Lambda > 0$ or $\Lambda = 0$ based on solving the Cauchy problem for a conformally invariant system of equations formed from the Fefferman-Graham (ambient obstruction) tensor.

In a joint work with Bob Kohn, we give a new control-type interpretation on the level-set approach to motion by curvature and related interface motion laws. More precisely, we give a family of discrete-time, two-person games whose value functions...

In joint work with J. Viaclovsky, we studied the problem of prescribing symmetric functions of the eigenvalues of the Schouten tensor for a conformal metric on a compact manifold (often referred to as the "Sigma-k Yamabe problem"). This is...

We will describe a result which extends the classical Coifman-Meyer theorem to the multi-parameter setting of polydiscs. This is based on work recently completed jointly with Jill Pipher, Terry Tao and Christoph Thiele.

I will talk about some recent joint work with Carlos Kenig on a certain type of uniqueness property for solutions of nonlinear Schrödinger equations on $R^d\times R$.