Related papers: The Schottky Conjecture and beyond
We give a generalization to convex co-compact semigroups of a beautiful theorem of Patterson-Sullivan, telling that the critical exponent (that is the exponential growth rate) equals the Hausdorff dimension of the limit set (that is the…
The basic theme of this paper is the fact that if $A$ is a finite set of integers, then the sum and product sets cannot both be small. A precise formulation of this fact is Conjecture 1 below due to Erd\H os-Szemer\'edi [E-S]. (see also…
We study a two-field model where a quintessence field with an exponential potential $e^{-\beta\phi/M_P}$ is coupled to the Higgs field. It is claimed that this model is consistent with the proposed Swampland conjecture. We check this claim…
Some recent studies based on numerical relativity simulations claim that slow contraction/ekpyrosis is strongly preferred over inflation as the smoothing mechanism that brought the universe into the homogeneous, isotropic and flat state we…
The large-scale structure growth index $\gamma$ provides a consistency test of the standard cosmology and is a potential indicator of modified gravity. We investigate the constraints on $\gamma$ from next-generation spectroscopic surveys,…
Based on the gauge potential decomposition theory and the $\phi $-mapping theory, the topological inner structure of the Chern-Simons-Higgs vortex has been showed in detail. The evolution of CSH vortices is studied from the topological…
Horndeski models with a de Sitter critical point for any kind of material content may provide a mechanism to alleviate the cosmological constant problem. Moreover, they could allow us to understand the current accelerated expansion of the…
Using the method of retarded potentials approximate formulas are obtained that describe the electromagnetic field outside the relativistic uniform system in the form of a charged sphere rotating at a constant speed. For the near, middle and…
We use the auxiliary fields and (excited-) de Sitter solutions to study the standard power spectrum of primordial fluctuations of a scalar field in the early universe. The auxiliary fields are the negative norm solutions of the field…
We propose and numerically validate a new fitting formula that is sufficiently accurate to model the growth of structure in Horndeski theories of modified gravity for upcoming Stage IV and V large-scale structure surveys. Based on an…
Coboundary and cosystolic expansion are notions of expansion that generalize the Cheeger constant or edge expansion of a graph to higher dimensions. The classical Cheeger inequality implies that for graphs edge expansion is equivalent to…
Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and…
We discuss the Singer conjecture and Gromov-L\"uck inequality $\chi \geq |\sigma|$ for aspherical complex surfaces. We give a proof of the Singer conjecture for aspherical complex surface with residually finite fundamental group that does…
In addition to topological lattice defects such as dislocations and disclinations, crystals are also accompanied by unavoidable ordinary defects, devoid of any non-trivial geometry or topology, among which vacancies, Schottky defects,…
The famous Bloch--Kato conjecture implies that for a field $F$ containing a primitive $p$th root of unity, the cohomology ring of the absolute Galois group $G_F$ of $F$ with $\mathbb{F}_p$ coefficients is generated by degree one elements.…
At the classical level the electromagnetic field can be well identified at the spatial infinity. Staruszkiewicz pointed out that the quantization of the electromagnetic field at spatial infinity is essentially unique and follows from the…
A modification of the ground state of the classical-spin Heisenberg Hamiltonian in the presence of a weak superstructural distortion of an otherwise Bravais lattice is examined. It is shown that a slight modulation of the crystal lattice…
We have examined the validity of the Gor'kov expansion in the strength of the order parameter of type II superconductors near the upper critical field. Although the degeneracy of the electron levels in a magnetic field gives non-…
In gauge theories, the physical, experimentally observable spectrum consists only of gauge-invariant states. This spectrum can be different from the elementary spectrum even at weak coupling and in the presence of the Brout-Englert-Higgs…
The Ooguri-Vafa Swampland Conjectures claim that in any consistent theory of quantum gravity, when venturing to large distances in scalar field space, a tower of particles will become light at a rate that is exponential in the field space…