Seminars Sorted by Series

In this talk I'll first go over some problems and related results in spectral geometry. Then I'll explain how one can apply Quantum Ergodicity and Bochner's theorem to prove that the number of nodal domains of quantum ergodic sequence of even...

In this talk I will present some new results on the structure of the zero sets of Schrödinger eigenfunctions on compact Riemannian manifolds. I will first explain how wiggly the zero sets can be by studying the number of intersections with a fixed...

In this talk I'll discuss a lattice point count for a thin semigroup inside $\mathrm{SL}_2(\mathbb Z)$. It is important for applications I'll describe that one can perform this count uniformly throughout congruence classes. The approach to counting...

The talk will be an introduction and a road map to the various connections the topic has with other areas of math and CS.

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...