Related papers: Bazzoni-Glaz Conjecture
We use type I string models with supersymmetry broken by compactification (\`a la Scherk-Schwarz) in order to test the weak gravity conjecture in the presence of runaway potentials in a perturbative string theory setting. For a finite value…
Barry Simon conjectured in 2005 that the Szeg\H{o} matrices, associated with Verblunsky coefficients $\{\alpha_n\}_{n\in\mathbb{Z}_+}$ obeying $\sum_{n = 0}^\infty n^\gamma |\alpha_n|^2 < \infty$ for some $\gamma \in (0,1)$, are bounded for…
A celebrated conjecture of Zs. Tuza says that in any (finite) graph, the minimum size of a cover of triangles by edges is at most twice the maximum size of a set of edge-disjoint triangles. Resolving a recent question of Bennett, Dudek, and…
Gamma conjecture I and the underlying Conjecture $\mathcal{O}$ for Fano manifolds were proposed by Galkin, Golyshev and Iritani recently. We show that both conjectures hold for all two-dimensional Fano manifolds. We prove Conjecture…
Hans Zassenhaus conjectured that every torsion unit of the integral group ring of a finite group $G$ is conjugate within the rational group algebra to an element of the form $\pm g$ with $g\in G$. This conjecture has been disproved recently…
A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological…
We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure $M$, Polish group $G$ of permutations of $M$, and $n \geq 1$,…
For a finite dimensional complex Lie algebra, its index is the minimal dimension of stabilizers for the coadjoint action. A famous conjecture due to Elashvili says that the index of the centralizer of an element of a reductive Lie algebra…
Let $p$ be an odd prime number and $k$ an imaginary quadratic field in which $p$ splits. In this paper, we consider a weak form of Greenberg's generalized conjecture for $p$ and $k$, which states that the non-trivial Iwasawa module of the…
Weakly generalised alternating knots are knots with an alternating projection onto a closed surface in a compact irreducible 3-manifold, and they share many hyperbolic geometric properties with usual alternating knots. For example, usual…
We propose a generalized formulation of the Scalar Weak Gravity Conjecture (SWGC) based on the analogy with the derivation of the Gauge Weak Gravity Conjecture (GWGC). We discuss some phenomenological implications of this Generalized SWGC,…
The power spectrum of weak lensing fluctuations has a non-Gaussian distribution due to its quadratic nature. On small scales the Central Limit Theorem acts to Gaussianize this distribution but non-Gaussianity in the signal due to…
Models with a scalar field coupled to the Gauss-Bonnet Lagrangian appear naturally from Kaluza-Klein compactifications of pure higher-dimensional gravity. We study linear, cosmological perturbations in the limits of weak coupling and…
Let Z be a subvariety of the moduli space of principally polarised abelian varieties of dimension g over the complex numbers. Suppose that Z contains a Zariski dense set of points which correspond to abelian varieties from a single isogeny…
The Lagrange-d'Alembert equations with constraints belonging to $H^{1,\infty}$ have been considered. A concept of weak solutions to these equations has been built. Global existence theorem for Cauchy problem has been obtained.
We study the constraints on gravity scale $M_P$ in extra-dimension gravitational theory, obtained from gravity-induced processes. The obtained constraints are subdivided into strong (though not robust) and reliable (though less strong). The…
In General Relativity (GR), the graviton is massless. However, a common feature in several theoretical alternatives of GR is a non-zero mass for the graviton. These theories can be described as massive gravity theories. Despite many…
In this paper, we define new fractal dimensions of a metric space in order to calculate the roughness of a set on a large scale. These fractal dimensions are called upper zeta dimension and lower zeta dimension. The upper zeta dimension is…
In studying Nakayama's 1958 conjecture on rings of infinite dominant dimension, Auslander and Reiten proposed the following generalization: Let Lambda be an Artin algebra and M a Lambda-generator such that Ext^i_Lambda(M,M)=0 for all i \geq…
We construct Zollfrei Lorentzian metrics on every nontrivial orientable circle bundle over a orientable closed surface. Further we prove a weaker version of Guillemin's conjecture assuming global hyperbolicity of the universal cover.