Seminars Sorted by Series

We present a Hamiltonian framework for higher-dimensional vortex filaments (or membranes) and vortex sheets as singular 2-forms with support of codimensions 2 and 1, respectively, i.e. singular elements of the dual to the Lie algebra of divergence...

We review some recent developments in KAM theory. By exploiting some identities of a geometric nature, one can obtain iterative steps which lead to numerical algorithms and which can follow the tori till breakdown. We present theoretical results in...

I will discuss a middle-dimensional generalization of Gromov's Non-Squeezing Theorem.

We study particular solutions of the "inner equation" associated to the splitting of separatrices on "generalized standard maps". An exponentially small complete expression for their difference is obtained. We also provide numerical evidence that...

This is a series of 3 talks on the topology of Stein manifolds, based on work of Eliashberg since the early 1990ies. More specifically, I wish to explain to what extent Stein structures are flexible, i.e. obey an h-principle. After providing some...

In 1964 Arnold constructed an example of instabilities for nearly integrable systems and conjectured that generically this phenomenon takes place. There has been big progress attacking this conjecture in the past decade. Jointly with Ke Zhang we...

In 1964 Arnold constructed an example of instabilities for nearly integrable systems and conjectured that generically this phenomenon takes place. There has been big progress attacking this conjecture in the past decade. Jointly with Ke Zhang we...

We shall discuss billiard dynamics in convex billiard tables in R^n.

In particular, we will describe a "symplectic point of view" which can be used, for example, to study the length of the shortest periodic billiard trajectory.

We shall discuss some basic results on surface diffeomorphisms. Then we introduce some results which were studied by both symplectic method and dynamical method. Finally we introduce some related questions.

Through geometrical models, perturbation techniques and sometimes analytical approaches, it has been possible to establish a dictionary between "a taxonomy of generic dynamical phenomenons" and a list of "simple mechanisms or dynamical...

I will talk about Ginzburg and Gurel's work on Hamiltonian pseudo-rotations of projective spaces, in particular, their proof of no fixed point of a pseudo-rotation of projective space is isolated as an invariant set.

This is a survey talk. The goal is to describe recent developments in Celestial Mechanics obtained with techniques from Symplectic Dynamics, and discuss open problems. Emphasis will be given to the construction of transverse foliations and their...

In this survey talk I will describe developments in the study of the planar circular restricted 3-body problem that were made possible through the use of pseudo holomorphic curves, following the theory developed by Hofer, Wysocki and Zehnder.

We will discuss several examples where ideas from persistent homology have applications to the study of the coarse geometry of groups of Hamiltonian diffeomorphisms, equipped with the Hofer norm..

The key idea is to consider Hamiltonian Floer...

I will talk about Ginzburg and Gurel's work on Hamiltonian pseudo-rotations of projective spaces, in particular, their proof of no fixed point of a pseudo-rotation of projective space is isolated as an invariant set.

I would like to discuss three topics concerning applications of holomorphic curve methods to the planar circular restricted three-body problem. The first is the existence of direct orbits and a conjecture due to Birkhoff. The second is the use of...

I will show that a closed, negatively curved Riemannian manifold of 1/4 pinched negative curvature has constant negative curvature if and only if the Lyapunov spectrum of its geodesic flow is the same as that of a hyperbolic manifold. The Lyapunov...

One of the most useful tools in quantifying the complexityof a dynamical system are the concepts of topological and metricentropy. While relevant in several contexts, entropy plays aparticularly important role in describing the behaviour of...

We consider the elliptic restricted three-body problem as a perturbation of the circular problem, with the perturbation parameter being the eccentricity of the orbits of the primaries. We show that for every suitably small, non-zero perturbation...

I will discuss some technical details regarding properties of feral pseuodoholomorphic curves, specifically those properties arising from stretching constructions and as components of limit buildings arising from attempts to compactify certain...

Semitoric systems are a type of 4-dimensional integrable system which has been classified by Pelayo-Vu Ngoc in terms of five invariants, one of which is a family of polygons generalizing the Delzant polygons which classify 4-dimensional toric...

A symplectic Lie groupoid is a Lie groupoid with a multiplicative symplectic form. We take the perspective that such an object is symplectic manifold with an extra categorical structure. Applying the machinery of Floer theory, the extra structure is...

In this talk, which reports on joint work with Jungsoo Kang, we formulate a local systolic inequality for Reeb flows and Hamiltonian diffeomorphisms, which we establish in low dimension. As a consequence, we derive bounds for the minimal magnetic...

For G a Lie group acting on a symplectic manifold and preserving a pair of Lagrangians, we use techniques from infinity category theory to construct a G-equivariant Floer homology of L0 and L1 without equivariant transversality. We give a sample...

Given a Weinstein domain $M$ and a compactly supported, exact symplectomorphism $\phi$, one can construct the open symplectic mapping torus $T_\phi$. Its contact boundary is independent of $\phi$ and thus $T_\phi$ gives a Weinstein filling of $T_0...

An outstanding problem in smooth ergodic theory is the estimation from below of Lyapunov exponents for maps which exhibit hyperbolicity on a large but non- invariant subset of phase space. It is notoriously difficult to show that Lypaunov exponents...

For Legendrian and transverse links in the 3-sphere, Ozsvath, Szabo, and Thurston defined combinatorial invariants that reside in grid homology. Known as the GRID invariants, they are effective in distinguishing some transverse knots that have the...

An area-preserving diffeomorphism of an annulus has an "action function" which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while...

We discuss recent developments in establishing uniform bounds on the spectral norm and related invariants in the absolute and relative settings. In particular, we describe new progress on a conjecture of Viterbo asserting such bounds for exact...

Hamiltonian homeomorphisms are those homeomorphisms of a symplectic manifold which can be written as uniform limits of Hamiltonian diffeomorphisms. One difficulty in studying Hamiltonian homeomorphisms (particularly in dimensions greater than two)...

In this survey talk, I will review the known constructions of mathematical theories of gauged sigma model and its relations with Gromov--Witten theory and FJRW theory. I will emphasize the analytic side, but will also mention related algebraic...

I'll outline the construction of an invariant for knots in homology 3-spheres which can be thought of as an SL(2,C) analog of Kronheimer and Mrowka's singular knot instanton homology. This invariant is similar to an invariant of 3-manifolds...

Analogous to Weinstein structures in symplectic geometry, there is a notion of convex structures in contact geometry. We discuss an explicit surgery theory for contact manifolds with convex structures, showing that they naturally decompose into...

I will describe a new family of symplectic capacities defined using rational symplectic field theory. These capacities are defined in every dimension and give state of the art obstructions for various "stabilized" symplectic embedding problems such...

It is conjectured that contact manifolds admitting flexible fillings have unique exact fillings. In this talk, I will show that exact fillings (with vanishing first Chern class) of a flexibly fillable contact (2n-1)-manifold share the same product...

I will discuss some current joint work with Helmut Hofer, in which we define and establish properties of a new class of pseudoholomorhic curves (feral J-curves) to study certain divergence free flows in dimension three. In particular, we show that...

I will discuss joint work with Hutchings which constructs nonequivariant and a family floer equivariant version of contact homology. Both theories are generated by two copies of each Reeb orbit over Z and capture interesting torsion information. I...

I will explain a polyfold proof, joint with Katrin Wehrheim, of the Arnold conjecture: the number of 1-periodic orbits of a nondegenerate 1-periodic Hamiltonian on a closed symplectic manifold is at least the sum of the Betti numbers. Our proof is a...