Related papers: Explicit characterization of the identity configur…
Atiyah classifies vector bundles on elliptic curves $E$ over an algebraically closed field of any characteristic. On the other hand, a rank $2$ vector bundle on $E$ defines a surface $S$ with a $\mathbb{P}^1$-bundle structure on $E$. We…
The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…
A scenario to understand the asymptotic properties of confinement between quark probes, based on a 4D mixed ensemble of percolating center-vortex worldsurfaces and chains, was initially proposed by one of us in a non-Abelian setting. More…
We define the symmetric (outer) automorphism group of a right-angled Artin group and construct for it a (spine of) Outer space. This `symmetric spine' is a contractible cube complex upon which the symmetric outer automorphism group acts…
Let $A$ be an abelian variety over an algebraically closed field. We show that $A$ is the automorphism group scheme of some smooth projective variety if and only if $A$ has only finitely many automorphisms as an algebraic group. This…
In this paper we develop a theory of convexity for a free Abelian group M (the lattice of integer points), which we call theory of discrete convexity. We characterize those subsets X of the group M that could be call "convex". One property…
This paper shows that simplicial oriented geometries can be characterized as groupoids with root systems having certain favorable properties, as conjectured by the first author. The proof first translates Handa's characterization of…
Classifying symmetry groups which can be implemented in the scalar sector of a model with $N$ Higgs doublets is a difficult and an unsolved task for $N>2$. Here, we make the first step towards this goal by classifying the Abelian symmetry…
In this paper we solve a long-standing problem which goes back to Laurent Schwartz's work on mean periodic functions. Namely, we completely characterise those locally compact Abelian groups having spectral synthesis. So far a…
The abelian Higgs model on a compact Riemann surface \Sigma supports vortex solutions for any positive vortex number d \in \ZZ. Moreover, the vortex moduli space for fixed d has long been known to be the symmetrized d-th power of \Sigma, in…
A new set of mathematical identities is presented for axi-symmetric sessile drops on flat and curved substrates. The geometrical parameters, including the apex curvature and height, and the contact radius, are related by the identities. The…
A square complex is a 2-complex formed by gluing squares together. This article is concerned with the fundamental group $\Gamma$ of certain square complexes of nonpositive curvature, related to quaternion algebras. The abelian subgroup…
We prove an identity for five arguments, valid in the lattice of natural numbers with gcd and lcm as lattice operations. More generally, this identity characterizes arbitrary distributive lattices. Fixing three of the five arguments, we…
We derive several identities that feature irreducible characters of the general linear, the symplectic, the orthogonal, and the special orthogonal groups. All the identities feature characters that are indexed by shapes that are "nearly"…
Cut-and-project sets $\Sigma\subset\mathbb{R}^n$ represent one of the types of uniformly discrete relatively dense sets. They arise by projection of a section of a higher-dimensional lattice to a suitably oriented subspace. Cut-and-project…
The main result of this paper is a rigorous proof of criticality and an explicit computation of critical exponents for the decay of avalanches in the Abelian sandpile model (ASM) on a large family of infinite graphs. We begin by introducing…
We study the surface roughness of prototype models displaying self-organized criticality (SOC) and their noncritical variants in one dimension. For SOC systems, we find that two seemingly equivalent definitions of surface roughness yields…
The space $D$ of Hodge structures on a fixed polarized lattice is known as Griffiths period domain and its quotient by the isometry group of the lattice is the moduli of polarized Hodge structures of a fixed type. When $D$ is a Hermition…
It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…
We study the category $\mathcal{A}$ of smooth semilinear representations of the infinite symmetric group over the field of rational functions in infinitely many variables. We establish a number of results about the structure of…