Related papers: La propriete de decroissance rapide pour le groupe…
We study the geometry of infinitely presented groups satisfying the small cancelation condition C'(1/8), and define a standard decomposition (called the criss-cross decomposition) for the elements of such groups. We use it to prove the…
We consider bicrossed products obtained by twisting compact semi-direct products by a suitable finite subgroup. Under some restriction, we give a practical criterion for the discrete dual of such bicrossed products to have the rapid decay…
The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers $\beta$ having the negative finiteness property, that is the set of finite $(-\beta)$-expansions is equal to…
We provide a new, dynamical criterion for the radial rapid decay property. We work out in detail the special case of the group $\Gamma := \mathbf{SL}_2(A)$, where $A := \mathbb{F}_q[X,X^{-1}]$ is the ring of Laurent polynomials with…
We study the supercurrent decay of a Bose-Einstein condensate in a ring trap combined with a repulsive barrier potential. In recent experiments, Kumar {\it et al.} [Phys. Rev. A {\bf 95}, 021602(R) (2017)] have measured the dependence of…
The fundamental group of a closed irreducible 3-dimensional manifold has the Rapid Decay property if and only if it is not virtually Sol. This is proved by studying distortion of length functions in graphs of groups, and the stability of…
We provide examples of groups with transcendental spectral radius: We first construct finitely presented examples, using links between decidability of the Word Problem and semi-computability of the spectral radius. This argument extends to…
Some well known results by Haagerup, Jolissaint and de la Harpe may be extended to the setting of a reduced crossed product of a C*-algebra A by a discrete group $G.$ We show that for many discrete groups, which include Gromov's hyperbolic…
The decay rates for the exclusive B decays $B \rightarrow K \eta_c $ and $B \rightarrow K^* \eta_c$ are calculated in the context of the heavy quark effective theory. We obtain $\Gamma (B \rightarrow K \eta_c )/\Gamma (B\rightarrow K\psi…
We show that small normal subsets $A$ of finite simple groups expand very rapidly -- namely, $|A^2| \ge |A|^{2-\epsilon}$, where $\epsilon >0$ is arbitrarily small.
In this paper we study the properties of diquarks (composed of $u$ and/or $d$ quarks) in the Bethe-Salpeter formalism under the covariant instantaneous approximation. We calculate their BS wave functions and study their effective…
We show that Wise's power alternative is stable under certain group constructions, use this to prove the power alternative for new classes of groups, and recover known results from a unified perspective. For groups acting on trees, we…
In this paper we study the Witt groups of symmetric and anti-symmetric forms on perverse sheaves on a finite-dimensional topologically stratified space with even dimensional strata. We show that the Witt group has a canonical decomposition…
In the seminal paper of Borel and Tits about reductive groups, they show some fundamental results about Bruhat cells with respect to a minimal parabolic subgroup, e.g., relative Bruhat decomposition and its geometrization, relative Bruhat…
We say that an abelian variety is degenerate if its Hodge ring is not generated by divisor classes. Degeneracy leads to some interesting challenges when computing Sato-Tate groups, and there are currently few examples and techniques…
These lectures are centered around a specific problem, the effect of weak repulsive interactions on the transition temperature $T_c$ of a Bose gas. This problem provides indeed a beautiful illustration of many of the techniques which have…
We propose to study a natural version of Connes' Rigidity Conjecture that involves property (T) groups with infinite center. Utilizing techniques at the intersection of von Neumann algebras and geometric group theory, we establish several…
In this paper, we provide several instances in which interesting approximation and stability properties are inherited by quotients with respect to finitely generated normal subgroups or, more strongly, normal subgroups with Kazhdan's…
We study the rapid decay property and polynomial growth for duals of bicrossed products coming from a matched pair of a discrete group and a compact group
We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the…