Related papers: Formality of the chain operad of framed little dis…

We introduce two topological non-$\Sigma$ operad structures on planar line arrangements subject to a certain geometric order condition, ensuring a well-defined notion of particle ordering on a distinguished line. This is interpreted in…

We give a combinatorial proof of a theorem of Gromov, which extends the scope of small cancellation theory to group presentations arising from labelled graphs.

We present a first step towards the Coq implementation of the Theory of Tagged Objects formalism. The concept of tagged types is encoded, and the soundness proofs are discussed with some future work suggestions.

We give a formalism of mixed sheaves on varieties over a subfield of the complex number field.

A Nikishin-Maurey characterization is given for bounded subsets of weak-type Lebesgue spaces. New factorizations for linear and multilinear operators are shown to follow.

We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are sorted by type.

This paper examines operad structures derived from poset matrices by formulating a set of new construction rules for poset matrices. In this direction, eleven different partial composition operations will be introduced as the basis for the…

We introduce a generalization of the notion of operad that we call a contractad, whose set of operations is indexed by connected graphs and whose composition rules are numbered by contractions of connected subgraphs. We show that many…

Relations between some kinds of formal and standard smoothness, for morphisms of schemes, are clarified in surprisingly simple and direct ways, bypassing much of the customarily employed machinery. Even the deep local-to-global property of…

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

Let $\mathfrak{X}$ be a smooth connected $p$-adic formal scheme. Based on the prismatic description of crystalline local systems, we prove an analogue of Fontaine's conjecture for torsion crystalline local systems on the generic fiber of…

We describe the construction of the slice fibration of a given one.

A formal theory based on a binary operator of directional associative relation is constructed in the article and an understanding of an associative normal form of image constructions is introduced. A model of a commutative semigroup, which…

We develop the theory of motivic integration for formal schemes

In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the…

We extend the formalism of I to a global setting for which a theorem on fiber integrals and a Fubini theorem are obtained. We compare our formalism to the previous constructions of motivic integration in the geometric and arithmetic cases.

These notes, based on the mini-course given at the PQR2003 Euroschool held in Brussels in 2003, aim to review Kontsevich's formality theorem together with his formula for the star product on a given Poisson manifold. A brief introduction to…

This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We…

A family of partial functions of a class of algebras $\mathsf{K}$ is said to be an implicit operation of $\mathsf{K}$ when it is defined by a first order formula and it is preserved by homomorphisms. In this work, we develop the theory of…

Formalism of extended Lagrangian represent a systematic procedure to look for the local symmetries of a given Lagrangian action. In this work, the formalism is discussed and applied to a field theory. We describe it in detail for a field…