Related papers: Chabauty Limits of Fermat Spirals

The one-loop beta functions for systems of $N_s$ scalars and $N_f$ fermions interacting via a general potential are analysed as tensorial equations in $4-\varepsilon$ dimensions. Two distinct bounds on combinations of invariants constructed…

For a definable continuous mapping $f$ from a definable connected open subset $\Omega$ of $\mathbb R^n$ into $\mathbb R^n,$ we show that the following statements are equivalent: (i) The mapping $f$ is open. (ii) The fibers of $f$ are finite…

In a recent paper by a superset of the authors it was proved that for every primitive 3-constrained space $\Gamma$ of finite diameter $\delta$ from Cherlin's catalogue of metrically homogeneous graphs, there exists a finite family $\mathcal…

We consider in this article an Elephant Random Walk evolving in the plane. Specifically, this is a reinforced stochastic process in which the $n$th step is given by a random rotation of one of the previous steps chosen uniformly at random.…

We show that the typical nonexpansive mapping on a small enough subset of a CAT($\kappa$)-space is a contraction in the sense of Rakotch. By typical we mean that the set of nonexpansive mapppings without this property is a $\sigma$-porous…

Note that the family of closed curves C_N={(x,y)\in R^2;x^(2N)+y^(2N)=1} for N=1,2,3,... approaches the boundary of [-1,1]^2 as N \to \infty. In this paper we exhibit a natural parameterization of these curves and generalize to a larger…

In this paper we consider strata of flat metrics coming from quadratic differentials (semi-translation structures) on surfaces of finite type. We provide a necessary and sufficient condition for a set of simple closed curves to be…

We study a class of 4-dimensional $SU(N)$ chiral gauge theories with fermions in the 2-index symmetric and antisymmetric representations and classify their infrared phases. The choice $N=4\mathbb{Z}$ corresponds to gauging the fermion…

Forbidden Patterns Problems (FPPs) are a proper generalisation of Constraint Satisfaction Problems (CSPs). However, we show that when the input is connected and belongs to a class which has low tree-depth decomposition (e.g. structure of…

Efficient discretisations of gauge groups are crucial with the long term perspective of using tensor networks or quantum computers for lattice gauge theory simulations. For any Lie group other than U$(1)$, however, there is no class of…

Probing the size and shape of the absorbers that lie in front of the QSOs, in particular the Ly alpha forest, we analyze 785 absorption lines in spectra of five QSOs in close groupings: a pair and a triplet. Both QSO groups have been…

In this paper we show that for Riemannian manifolds with boundary the natural restriction map is a quasifibration between spaces of metrics of positive scalar curvature. We apply this result to study homotopy properties of spaces of such…

High resolution N-body simulations of cold dark matter (CDM) models predict that galaxies and clusters have cuspy halos with excessive substructure. Observations reveal smooth halos with central density cores. One possible resolution of…

According to a classical result of Szemer\'{e}di, every dense subset of $1,2,...,N$ contains an arbitrary long arithmetic progression, if $N$ is large enough. Its analogue in higher dimensions due to F\"urstenberg and Katznelson says that…

We show that the Hrushovski-\fraisse limit of certain classes of trees lead to strictly superstable theories of various U-ranks. In fact, for each $ \alpha\in\omega+1\backslash\{0\} $ we introduce a strictly superstable theory of U-rank $…

It is still debated whether the low-doping Fermi surface of cuprates is composed of hole pockets or of disconnected Fermi arcs. Results from cellular dynamical mean field theory (c-DMFT) support the Fermi arcs hypothesis by predicting…

We study the Schwinger-Dyson equation for the fermion self-energy in massless and massive $QED_2$, in the ladder approximation. When the fermion is massless (and the photon massless or massive), we check the reliability of this…

We develop the BRST approach to Lagrangian formulation for all massless half-integer higher spin fields on an arbitrary dimensional flat space. General procedure of Lagrangian construction describing the dynamics of fermionic field with any…

Let $\Gamma$ be a discrete subgroup of a simply connected, solvable Lie group~$G$, such that $\Ad_G\Gamma$ has the same Zariski closure as $\Ad G$. If $\alpha \colon \Gamma \to \GL_n(\real)$ is any finite-dimensional representation…

The observation of a sharp spectral feature in the gamma-ray sky would be one of the cleanest ways to identify dark matter and pinpoint its properties. Over the years a lot of attention has been paid to two specific features, namely…