Seminars Sorted by Series

The aim of this talk is to show that C*-algebras are useful for studying stability of groups. In particular we will discuss some obstructions for Hilbert-Schmidt stability of groups, obtain a complete characterization of Hilbert-Schmidt stability...

Some years ago, I proved with Shulman and Sørensen that precisely 12 of the 17 wallpaper groups are matricially stable in the operator norm. We did so as part of a general investigation of when group $C^*$-algebras have the semiprojectivity and weak...

This expository talk will try to bridge the first examples of "almost commuting" unitary matrices that are not almost "commuting unitaries" due to Voiculescu to a more sophisticated and very beautiful construction of examples by Gromov and Lawson in...

In [MIP*=RE by JNVWY] the authors construct a non-local game that resolves Tsirelson's problem to the negative and by that refute Connes' embedding conjecture (CEC). The game *-algebra (see e.g. [KPS]) enables one to construct a finitely presented *...

We study stability problems with respect to families of groups equipped with bi-invariant ultrametrics, that is, metrics satisfying the strong triangle inequality. This property has very strong consequences, and this form of stability behaves very...

We discuss various (still open) questions on approximations of finitely generated groups, focusing on finite-dimensional approximations such as residual finiteness and soficity. We survey our results on the existence, stability and quantification of...

In 1966 V. Arnold showed how solutions of the Euler equations of hydrodynamics can be viewed as geodesics in the group of volume-preserving diffeomorphisms. This provided a motivation to study the geometry of this group equipped with the $L^2$...

There are indications that in the 80s Guillemin posed a question: If billiard maps are conjugate, can we say that domains are the same up to isometry? On one side, we show that conjugacy of different domains can't be C^1 near the boundary. In...

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...