相关论文: Thin Elements and Commutative Shells in Cubical om…
There are several ways to construct omega-categories from combinatorial objects such as pasting schemes or parity complexes. We make these constructions into a functor on a category of chain complexes with additional structure, which we…
Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $\Sigma$ of genus $l >1$, the order of the group $H^2(\Sigma,\pi_1(G))$ is equal to the number of connected components of the…
A short survey of the semiclassical periodic orbit theory, initiated by M. Gutzwiller and generalized by many other authors, is given. Via so-called semiclassical trace formmulae, gross-shell effects in bound fermion systems can be…
We revisit the construction of the composite Higgs models in a context of the bottom-up holographic approach. The soft wall framework is under consideration imposing the translation of the $4D$ global symmetry breaking characteristic to the…
Orthogonality in model theory captures the idea of absence of non-trivial interactions between definable sets. We introduce a somewhat opposite notion of cohesiveness, capturing the idea of interaction among all parts of a given definable…
We show that for any type in Martin-L\"of Intensional Type Theory, the terms of that type and its higher identity types form a weak omega-category in the sense of Leinster. Precisely, we construct a contractible globular operad of definable…
A quasi-schemoid is a small category whose morphisms are colored with appropriate combinatorial data. In this note, Mitchell's embedding theorem for a tame schemoid is established. The result allows us to give a cofibrantly generated model…
Tropical geometry is a relatively recent field in mathematics created as a simplified model for certain problems in algebraic geometry. We introduce the definition of abstract and planar tropical curves as well as their properties,…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
In some models of electro-weak interactions the W and Z bosons are considered composites, made up of spin-one-half subconstituents. In these models a spin zero counterpart of the W and Z boson naturally appears, whose higher mass can be…
We study the quantum transition from a strongly correlated metal, with heavy fermionic quasiparticles, to a metal with commensurate charge or spin density wave order. To this end, we introduce and numerically analyze a large dimensionality…
We study possible strong first-order electroweak phase transitions in Composite Higgs models and we quantify the part of parameter space that can be probed with future gravitational Wave experiments. We focus on models where the Composite…
The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.
The structure of lamellar phases of symmetric $AB$ diblock copolymers in a thin film is investigated. We quantitatively compare the composition profiles and profiles of individual segments in self-consistent field calculations with Monte…
We find the connection between 3-dimensional commutative algebras with a trivial trace and plane quartics and its bitangents.
We theoretically explore the electronic structure of holes in cylindrical Germanium/Silicon core/shell nanowires using a perturbation theory approach. The approach yields a set of interpretable and transferable effective low-energy models…
We define the notion of whiskered categories and groupoids, showing that whiskered groupoids have a commutator theory. So also do whiskered $R$-categories, thus answering questions of what might be `commutative versions' of these theories.…
We construct a graph of Kummer elements in a given cyclic algebra of prime degree and study its properties. In case of degree 5, we provide sufficient conditions for two elements to have a chain of Kummer elements connecting them, such that…
In this survey article we describe some geometric results in the theory of noncommutative rings and, more generally, in the theory of abelian categories. Roughly speaking and by analogy with the commutative situation, the category of graded…
Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur…