Related papers: Notes on identical configurations in Abelian Sandp…
We define a higher-order generalisation of the CPM construction based on arbitrary finite abelian group symmetries of symmetric monoidal categories. We show that our new construction is functorial, and that its closure under iteration can…
These notes are intended to be a pedagogical introduction to higher-form symmetries, which are symmetries whose charged objects are extended operators supported on lines, surfaces, and etc. This subject has been one of the most popular and…
We extend to the topological setting the classical constructions of the Abel-Jacobi mapping on homologically trivial algebraic cycles and the height pairing between two such cycles. We further interpret the height pairing between…
In this note we give a theoretical support by means of quotient polynomial rings for the computation formulas of the dimension of abelian codes.
Let $ S $ be a quasi-projective smooth variety over complex field $ \mathbb{C} $. For a smooth projective morphism $ \pi:X\to S $, we will introduce a new height pairing \begin{align*} CH^p_{\hom}(X/S) \times CH^q_{\hom}(X/S) \to…
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
Several recent papers construct auxiliary polynomials to bound the Weil height of certain classes of algebraic numbers from below. Following these techniques, the author gave a general method for introducing auxiliary polynomials to…
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
The main object of this work is to present a powerful method of construction of subshifts which we use chiefly to construct WAP systems with various properties. Among many other applications of this so called labeled subshifts, we obtain…
For a paradigmatic case, the standard map, we discuss how the statistical description of the approach to equilibrium is related to the sensitivity to the initial conditions of the system. Using a numerical analysis we present an anomalous…
The author has recently introduced abstract algebraic frameworks of analogical proportions and similarity within the general setting of universal algebra. The purpose of this paper is to build a bridge from similarity to analogical…
In their previous work, the authors studied the abelian sandpile model on graphs constructed from a growing piece of a plane or space tiling, given periodic or open boundary conditions, and identified spectral factors which govern the…
The main purpose of this note is to establish the continuity of seminorms on finite-dimensional vector spaces over the real or complex numbers.
We consider the identity of the abelian sandpile group of finite approximation graphs of the Sierpinski gasket, and we show that the second-order term in the scaling limit converges to the path distance to the nearest corner on the…
In this paper we study abelian varieties which correspond to CM points in the coarse moduli space of principally polarized abelian varieties with multiplication by a maximal order in a quaternion algebra over a totally real number field.…
In this paper, we shall study the structure of walls for Bridgeland's stability conditions on abelian surfaces. In particular, we shall study the structure of walls for the moduli spaces of rank 1 complexes on an abelian surface with the…
We demonstrate equivalence between two definitions of lower finite highest weight categories. We also show that, in the presence of a duality, a lower finite highest weight structure on a category is unique. Finally, we give a new proof for…
Aim of this note is to extract cohomological information about the manifold $Emb(M,N)$ from the topology of the target manifold N. For special conditions, a monomorphism $H^1 (N) \to H^1 (Emb(M,N))$ is constructed.
We show that tilting modules and parity sheaves on the affine Grassmannian are related through the geometric Satake correspondence, when the characteristic is bigger than an explicit bound.
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…