Related papers: Stabilizers, groups with f-generics in NTP2 and PR…

We prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble…

We consider the three dimensional gravitational Vlasov-Poisson (GVP) system in both classical and relativistic cases. The classical problem is subcritical in the natural energy space and the stability of a large class of ground states has…

We classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space and Urysohn sphere, among other related results.

We prove a statement concerning hyperlinearity for central extensions of property (T) groups in the presence of flexible HS-stability, and more generally, weak ucp-stability. Notably, this result is applied to show that if $\text{Sp}_{2g}…

As a serious attempt for constructing a new foundation for describing micro-entities from a causal standpoint, it was explained before in [1, 2, 3] that by unifying the concepts of information, matter and energy, each micro-entity is…

We establish an entropy rigidity theorem for Hitchin representations of all geometrically finite Fuchsian groups which generalizes a theorem of Potrie and Sambarino for Hitchin representations of closed surface groups. In the process, we…

We prove an accessibility theorem for finite-index splittings of groups. Given a finitely presented group G there is a number n(G) such that, for every reduced locally finite G-tree T with finitely generated stabilizers, T/G has at most…

A generalization of the double commutator lemma for normal subgroups is shown for invariant random subgroups of a countable group acting faithfully on a Hausdorff space. As an application, we classify ergodic invariant random subgroups of…

We classify the stable formulas in the theory of Dense Linear Orders without endpoints, the stable formulas in the theory of Divisible Abelian Groups, and the stable formulas without parameters in the theory of Real Closed Fields. The third…

We prove that a finitely generated pro-$p$ group acting on a pro-$p$ tree $T$ with procyclic edge stabilizers is the fundamental pro-$p$ group of a finite graph of pro-$p$ groups with edge and vertex groups being stabilizers of certain…

We prove generic differentiability in $P$-minimal theories, strengthening an earlier result of Kuijpers and Leenknegt. Using this, we prove Onshuus and Pillay's $P$-minimal analogue of Pillay's conjectures on o-minimal groups. Specifically,…

Let k be a number field, p$\ge$2 a prime and S a set of tame or wild finite places of k. We call K/k a totally S-ramified cyclic p-tower if Gal(K/k)=Z/p^NZ and if S non-empty is totally ramified. Using analogues of Chevalley's formula…

We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zung's theorem) we give a shorter and more geometric proof, based on a Moser deformation…

An elementary introduction to the non-perturbative renormalization group is presented mainly in the context of statistical mechanics. No prior knowledge of field theory is necessary. The aim is this article is not to give an extensive…

We prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and a distal-like quotient.

In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. We extend it to pairs (f_1,f_2) of maps between manifolds of arbitrary dimensions, using nonstabilized normal bordism theory…

We analyze stabilization with respect to ${\mathbb P}^1$ in the Morel--Voevodsky unstable motivic homotopy theory. We introduce a refined notion of cellularity (a.k.a., biconnectivity) in various motivic homotopy categories taking into…

A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…

We give a characterization of isomorphisms between Schreier graphs in terms of the groups, subgroups and generating systems. This characterization may be thought as a graph analog of Mostow's rigidity theorem for hyperbolic manifolds. This…

The aim of this paper is to generalise the notion of p-stability to fusion systems. We study the question how Qd(p) is involved in finite simple groups. We show that with a single exception a simple group involving Qd(p) has a subgroup…