Related papers: Highly symmetric lines
We propose the definition of (twisted) generalized hyperkaehler geometry and its relation to supersymmetric non-linear sigma models. We also construct the corresponding twistor space.
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
The objects of study are triangulations of the dilated standard triangle in the plane. Motivated by work on T-curves (Geiselmann et al., 2026), the focus lies on unimodular triangulations with a fixed symmetry axis. Lower and upper bounds…
In terms of the derivative operator and three hypergeometric series identities, several interesting summation formulas involving generalized harmonic numbers are established.
We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and the characterisations of projective and unitary equivalence.…
This paper investigates the synchronization problems for general high-dimensional linear networks over finite fields. By using the technique of linear transformations and invariant subspaces for linear spaces over finite fields, several…
We focus on the geometrical reformulation of free higher spin supermultiplets in $4\rm{D},~\mathcal{N}=1$ flat superspace. We find that there is a de Wit-Freedman like hierarchy of superconnections with simple gauge transformations. The…
Zauner's conjecture concerns the existence of $d^2$ equiangular lines in $\mathbb{C}^d$; such a system of lines is known as a SIC. In this paper, we construct infinitely many new SICs over finite fields. While all previously known SICs…
We introduce a class of finite tight frames called prime tight frames and prove some of their elementary properties. In particular, we show that any finite tight frame can be written as a union of prime tight frames. We then characterize…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
Statistical ensembles of networks, i.e., probability spaces of all networks that are consistent with given aggregate statistics, have become instrumental in the analysis of complex networks. Their numerical and analytical study provides the…
We study aspects of 3d $\mathcal{N}=2$ supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the…
Transforming an asymmetric system into a symmetric system makes it possible to exploit the simplifying properties of symmetry in control problems. We define and characterize the family of symmetrizable systems, which can be transformed into…
We present an extension of the Delsarte linear programming method. For several dimensions it yields improved upper bounds for kissing numbers and for spherical codes. Musin's recent work on kissing numbers in dimensions three and four can…
Closed subschemes in projective space with a fixed Hilbert polynomial are parametrized by a Hilbert scheme. We classify the smooth ones. We identify numerical conditions on a polynomial that completely determine when the Hilbert scheme is…
We consider a class of line operators in d=4, N=2 supersymmetric field theories which leave four supersymmetries unbroken. Such line operators support a new class of BPS states which we call "framed BPS states." These include halo bound…
The regular polyhedra have the highest order of 3D symmetries and are exceptionally at- tractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass…
Algebraic number theory relates SIC-POVMs in dimension $d>3$ to those in dimension $d(d-2)$. We define a SIC in dimension $d(d-2)$ to be aligned to a SIC in dimension $d$ if and only if the squares of the overlap phases in dimension $d$…