Seminars Sorted by Series

We show that if $G=\langle S | E\rangle$ is a discrete group with Property (T) then $E$, as a system of equations over $S$, is not stable (under a mild condition). That is, $E$ has approximate solutions in symmetric groups $Sym(n)$, $n \geq 1$, that...

A countable group $G$ is called sofic if it admits a sofic approximation: a sequence of asymptotically free almost actions on finite sets. Given a sofic group $G$, it is a natural problem to try to classify all its sofic approximations and, more...

A sofic approximation to a countable discrete group is a sequence of finite models for the group that generalizes the concept of a Folner sequence witnessing amenability of a group and the concept of a sequence of quotients witnessing residual...

In this talk I will present a joint work with Arie Levit and Yair Minsky on flexible stability of surface groups. The proof will be geometric in nature and will rely on an analysis of branched covers of hyperbolic surfaces. Along the way we will see...

Let C be a class of groups. (For example, C is a class of all finite groups, or C is a class of all finite symmetric groups.) I give a definition of approximations of a group G by groups from C. For example, the groups approximable by symmetric...

Several well-known open questions (such as: are all groups sofic/hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups $Sym(n)$ (in the sofic case) or the finite dimensional unitary...

In his seminal paper from 1973, Garland introduced a machinery for proving vanishing of group cohomology for groups acting on Bruhat-Tits buildings. This machinery, known today as “Garland’s method”, had several applications as a tool for proving...

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.