Related papers: Sur le spectre des longueurs des groupes de triang…

Tiny fluctuations of the Cosmic Microwave Background as well as various observable quantities obtained by spin raising and spin lowering of the effective gravitational lensing potential of distant galaxies and galaxy clusters, are described…

We calculate the spectrum of the diagram for each finite $3$-transposition group. Such graphs with a given minimal eigenvalue have occurred in the context of compact Griess subalgebras of vertex operator algebras.

Observational constraints on standard CDM spectra and perturbation spectra with broken scale invariance are discussed.

The purpose of this paper is to investigate some properties of fuzzy ideals and fuzzy bi-ideals in gamma-semigroups and to introduce the notion of fuzzy quasi ideals in gamma-semigroups. Here we also characterize a regular gamma-semigroup…

We study the set of normalized multi-lengths for representations of closed surface groups and free groups into $(\mathrm{PSL}_2\mathbf{R})^d$ whose projections to $\mathrm{PSL}_2\mathbf{R}$ are all convex cocompact. These multi-lengths…

Using a Cayley complex (generalizing the Cayley graph) and Clifford algebras, we are able to give, for a large class of finitely presented groups, a uniform construction of spectral triples with $D_{+}$ of index 1.

We construct examples showing that the normalized Lebesgue measure of the conical limit set of a uniformly quasiconformal group acting discontinuously on the disc may take any value between zero and one. This is in contrast to the cases of…

We consider triangulations of surfaces with edges painted three colors so that edges of each triangle have different colors. Such structures arise as Belyi data (or Grothendieck dessins d'enfant), on the other hand they enumerate pairs of…

In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.

We prove a conjecture of R. Schwartz about the type of some complex hyperbolic triangle groups.

In this paper we prove the "Tiling implies Spectral" part of Fuglede's paper for the case of three intervals. Then we prove the "Spectral implies Tiling" part of the conjecture for the case of three equal intervals as also when the…

Some aspects of Cauchy integrals on sets with dimension larger than 1 are briefly discussed.

We summarize the status of a ``targeted'' redshift survey aimed at establishing the properties of galaxies and their large scale distribution in the redshift range 2.5 < z < 3.5. At the time of this writing, we have obtained spectra of more…

The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.

We discuss recent advances in the study of dusty, massive galaxies at z>1 arising from the first extensive spectroscopic surveys.

We consider Fuchsian singularities of arbitrary genus and prove, in a conceptual manner, a formula for their Poincar\'e series. This uses Coxeter elements involving Eichler-Siegel transformations. We give geometrical interpretations for the…

The main result of this paper is that the categories of (right) hypergroups over the group and of triples, consisting of a group, its subgroup and a (right) transversal to this subgroup, are equivalent.

This is an introduction to the finite groups, with focus on the groups of permutations and reflections, and more generally, on the finite groups of unitary matrices. We first discuss the basics of group theory, featuring the cyclic,…

In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…

We give new equations that axiomatize the variety of trimedial quasigroups. We also improve a standard characterization by showing that right semimedial, left F-quasigroups are trimedial.