Related papers: Tight closure's failure to localize - a self-conta…

We present a new approach to singularity confinement which makes it an efficient and reliable discrete integrability detector. Our method is based on the full-deautonomisation procedure, which consists in analysing non-autonomous extensions…

We reformulate the inequalities among self-closeness numbers of spaces in cofibrations making use of homology dimension and show that the self-closeness number of a space is less than or equal to the homology dimension of the space. Then we…

We construct algebraically closed fields containing an algebraic closure of the field of power series in several variables over a characteristic zero field. Each of these fields depends on the choice of an Abhyankar valuation and are…

The finite-degree Zariski (Z-) closure is a classical algebraic object, that has found a key place in several applications of the polynomial method in combinatorics. In this work, we characterize the finite-degree Z-closures of a subclass…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

This article studies the categorical setting of Abramsky, Haghverdi, and Scott's untyped linear combinatory algebras, and relates this to more recent work of Abramsky and Heunen on Frobenius algebras in the infinitary setting. The key to…

We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's…

We prove that the tight closure and the graded plus closure of a homogeneous ideal coincide for a two-dimensional N-graded domain of finite type over the algebraic closure of a finite field. This answers in this case a ``tantalizing…

This paper is concerned with the open problem proposed in Ammari et. al. Commun. Math.Phys, 2013. We first investigate the existence and uniqueness of Generalized Polarization Tensors (GPTs) vanishing structures locally in both two and…

We study a variant of the majorization relation. In particular we consider inequalities involving some Schur-concave symmetric polynomials related to the multinomial expansion. We also discuss how these topics were motivated by conjectures…

We extend some classical results - such as Quillen's Theorem A, the Grothendieck construction, Thomason's Theorem and the characterisation of homotopically cofinal functors - from the homotopy theory of small categories to polynomial monads…

Given a combinatorial triangulation of an $n$-gon, we study (a) the space of all possible drawings in the plane such the edges are straight line segments and the boundary has a fixed shape, and (b) the algebraic variety of possibilities for…

We present a finitary version of Moss' coalgebraic logic for $T$-coalgebras, where $T$ is a locally monotone endofunctor of the category of posets and monotone maps. The logic uses a single cover modality whose arity is given by the least…

Using an approach to the Jacobian Conjecture by L.M. Dru\.zkowski and K. Rusek 12], G. Gorni and G. Zampieri [19], and A.V. Yagzhev[27], we describe a correspondence between finite dimensional symmetric algebras and homogeneous tuples of…

We give an elementary introduction to some recent polyhedral techniques for understanding and solving systems of multivariate polynomial equations. We provide numerous concrete examples and illustrations, and assume no background in…

We establish isomorphisms between certain specializations of Birman-Murakami-Wenzl algebras and the symmetric squares of Temperley-Lieb algebras. These isomorphisms imply a link-polynomial identity due to W. B. R. Lickorish. As an…

We extend to infinite dimensional Hilbert spaces a celebrated result, due to B. Polyak, about the convexity of the joint image of quadratic functions. We give sufficient conditions which assure that the joint image is also closed. However,…

We argue that Kantor and Kardar's assertion that their simulation results contradict our criterion for the localization of a softly constrainted ideal polymer is incorrect. Our criterion is inapplicable to the model used in these…

This paper studies cluster algebras locally, by identifying a special class of localizations which are themselves cluster algebras. A `locally acyclic cluster algebra' is a cluster algebra which admits a finite cover (in a geometric sense)…

We study numerically the tightness of prime flat knots in a model of self-attracting polymers with excluded volume. We find that these knots are localised in the high temperature swollen regime, but become delocalised in the low temperature…