相关论文: Cubical Covers of Sets in $\mathbb{R}^n$

We have two parallel goals of this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the…

We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topology and algebraic geometry, such as dimension and defining…

The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…

In this article, we prove some subsets of the set of natural numbers $\mathbb{N}$ and any non-zero ideals of an order of imaginary quadratic fields are fractionally dense in $\mathbb{R}_{>0}$ and $\mathbb{C}$ respectively.

Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of…

We prove the bounded packing property for any abelian subgroup of a group acting properly and cocompactly on a CAT(0) cube complex. A main ingredient of the proof is a cubical flat torus theorem. This ingredient is also used to show that…

We study optimal simple second-order cone representations (a particular subclass of second-order cone representations) for weighted geometric means, which turns out to be closely related to minimum mediated sets. Several lower and upper…

Analytical and numerical methods are developed to analyze the quantum nature of the big bang in the setting of loop quantum cosmology. They enable one to explore the effects of quantum geometry both on the gravitational and matter sectors…

This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but…

We propose a definition of expander representations of quivers, generalizing dimension (or linear algebra) expanders, as a qualitative refinement of slope stability. We prove existence of uniform expander representations for any wild quiver…

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…

We study the rotation sets for homeomorphisms homotopic to the identity on the torus $\mathbb T^d$, $d\ge 2$. In the conservative setting, we prove that there exists a Baire residual subset of the set $\text{Homeo}_{0, \lambda}(\mathbb…

We provide sufficient conditions as to when a boundary component of a cocompact convex set in a CAT(0)-space is contractible. We then use this to study when the limit set of a quasi-convex, codimension one subgroup of a negatively curved…

In representation theory, the problem of classifying pairs of matrices up to simultaneous similarity is used as a measure of complexity; classification problems containing it are called wild problems. We show in an explicit form that this…

We investigate the asymptotic properties of random polytopes arising as convex hulls of $n$ independent random points sampled from a family of block-beta distributions. Notably, this family includes the uniform distribution on a product of…

Polystability of (twisted) Stokes representations (i.e. wild monodromy representations) will be characterised, in terms of the corresponding differential Galois group (generalising the Zariski closure of the monodromy group in the tame…

Quantum Electrodynamics (QED) serves as a useful toy model for classical observables in gravitational two-body systems with reduced complexity due to the linearity of QED. We investigate scattering observables in scalar QED at the sixth…

A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some…

The notion of a tamely ramified covering is canonical only for curves. Several notions of tameness for coverings of higher dimensional schemes have been used in the literature. We show that all these definitions are essentially equivalent.…

Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…