Related papers: Chabauty Limits of Fermat Spirals

We show that badly approximable matrices are exactly those that, for any inhomogeneous parameter, can not be inhomogeneous approximated at every monotone divergent rate, which generalizes Ram\'irez's result (2018). We also establish some…

Any mu^2-divergence is shown analytically to be absent for a class of actions for Overlap and Domain Wall Fermions with nonzero chemical potential. All such actions are, however, shown to violate the chiral invariance. While the parameter M…

A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in…

Simulations of large-scale structure formation predict the formation of sheet- and filamentary structures, which are often invoked as the origin of the Lyman-alpha forest. In their simplest description, these sheets and filaments require a…

We prove that there are only finitely many isoparametrically foliated closed connected Riemannian manifolds with bounded geometry, fixed dimension $n\neq5$, and finite fundamental group, up to foliated diffeomorphism. In addition, we…

A closed-form formula is derived for the number of occurrences of matches of a multiset of patterns among all ordered (plane-planted) trees with a given number of edges. A pattern looks like a tree, with internal nodes and leaves, but also…

We generalise the study of fermionic and bosonic entanglement in non-inertial frames to fields of arbitrary spin and beyond the single mode approximation. After the general analysis we particularise for two interesting cases: entanglement…

We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree $n>2$ up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The…

A subset $\Sigma \subset F_N$ of the free group of rank $N$ is called \emph{spectrally rigid} if whenever trees $T, T'$ in Culler-Vogtmann Outer Space are such that $\| g \|_T = \| g \|_{T'}$ for every $g \in \Sigma$, it follows that $T =…

In this paper, we will show that strong approximation with Brauer-Manin obstruction holds for certain quadratic fibration such that none of fibers satisfies strong approximation with Brauer-Manin obstruction. Moreover, we develop the…

Strongly bounded groups are those groups for which every action by isometries on a metric space has orbits of finite diameter. Many groups have been shown to have this property, and all the known infinite examples so far have cardinality at…

The Fermat type Calabi-Yau $n$-fold, denoted by $\mathscr{F}_n$, is the hypersurface of $\mathbb{P}^{n+1}$ defined by $\sum_{i=0}^{n+1}x_i^{n+2}=0$, which is the smooth fiber over the Fermat point $\psi=0$ of the Fermat pencil $$…

Let $G$ be a unipotent group and $\mathcal F=\{F_t:t\in (0,\infty)\}$ a family of subsets of $G$, with $\mathcal F$ definable in an o-minimal expansion of the real field. Given a lattice $\Gamma\subseteq G$, we study the possible Hausdorff…

We show that limits for the critical exponent tending to \infty exist in both critical circle homeomorphisms of golden mean rotation number and Fibonacci circle coverings. Moreover, they are the same. The limit map is not analytic at the…

The trace set of a Fuchsian group $\Gamma$ ist the set of length of closed geodesics in the surface $\Gamma \backslash \mathbb{H}$. Luo and Sarnak showed that the trace set of a cofinite arithmetic Fuchsian group satisfies the bounded…

The gravitational spin connection appears in gravity as a non-Abelian gauge field for the Lorentz group $SO(3,1)$, which is non-compact. The action for General Relativity is linear in the field strength associated to the spin connection,…

We show that every limit point of a Zariski dense discrete subgroup $\Gamma$ of the isometry group of a symmetric space of noncompact type is conical if and only if $\Gamma$ is convex cocompact.

The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping $f\mapsto \widehat{f\sigma}$ is bounded from $\lt(S^2)$ to $L^4(\reals^3)$. We prove that there exist functions which extremize this inequality, and that…

We give a short proof of the following result due to Howie: if $A(\Gamma)$ is a right-angled Artin group embedding into some one-relator group, then $\Gamma$ is a finite forest. The proof only uses elementary Bass--Serre theory and…

We present results from a survey of the Lyman alpha forest at 2.15<z<3.26 toward ten QSOs concentrated within a 1 degree field. We find correlations of the Lyman alpha absorption line wavelengths between different lines-of-sight over the…