Related papers: The Classification of Exceptional CDQL Webs on Com…
The set SL(n) of n-string links has a monoid structure, given by the stacking product. When considered up to concordance, SL(n) becomes a group, which is known to be abelian only if n=1. In this paper, we consider two families of…
Given a semisimple Lie algebra $\mathfrak{g}$, we can represent invariants of tensor products of fundamental representations of the quantum enveloping algebra $U_q(\mathfrak{g})$ using particular directed graphs called webs. In particular…
In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal to the dimension can be modeled by the cohomology of an…
We give various results and applications using the connection $(E,\nabla)$ associated with a $d$-web. Precisely, we exhibit fundamental invariants of the web related to the differential equation of first order which presents the web. They…
The Gronwall conjecture states that a planar 3-web of foliations which admits more than one distinct linearizations is locally equivalent to an algebraic web. We propose an analogue of the Gronwall conjecture for the 3-web of foliations by…
We introduce web supercategories of type Q. We describe the structure of these categories and show they have a symmetric braiding. The main result of the paper shows these diagrammatically defined monoidal supercategories provide…
Let $\mathbb{k}$ be a characteristic zero domain. For a locally unital $\mathbb{k}$-superalgebra $A$ with distinguished idempotents $I$and even subalgebra $a \subseteq A_{\bar 0}$, we define and study an associated diagrammatic monoidal…
We study four-dimensional N=1 gauge theories which arise from D3-brane probes of toric Calabi-Yau threefolds. There are some standing paradoxes in the literature regarding relations among (p,q)-webs, toric diagrams and various phases of the…
We study local ($n+1$)-webs of codimension 1 on a manifold of dimension $n.$ We give a complete description of their possible Lie algebras of infinitesimal diffeomorphisms. More precisely we show that these Lie algebras are direct products…
Bondal and Kapranov describe how to assign to a full exceptional collection on a variety X a DG category C such that the bounded derived category of coherent sheaves on X is equivalent to the bounded derived category of C. In this paper we…
We consider singular Q-acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is C^1- or C*-ruled or the surface is up to isomorphism one of two…
An abelian cover is a finite morphism $X\to Y$ of varieties which is the quotient map for a generically faithful action of a finite abelian group $G$. Abelian covers with $Y$ smooth and $X$ normal were studied in…
Generalizing the polynomial web category, we introduce a diagrammatic $\Bbbk$-linear monoidal category, the affine web category, for any commutative ring $\Bbbk$. Integral bases consisting of elementary diagrams are obtained for the affine…
This thesis proposes a framework based on a notion of combinatorial cell complex (cc) whose cells are defined simply as finite sets of vertices. The cells of a cc are subject to four axioms involving a rank function that assigns a rank (or…
An almost Abelian Lie group is a non-Abelian Lie group with a codimension 1 Abelian subgroup. We show that all discrete subgroups of complex simply connected almost Abelian groups are finitely generated. The topology of connected almost…
We study $d$-dimensional simplicial complexes that are PL embeddable in $\mathbb{R}^{d+1}$. It is shown that such a complex must satisfy a certain homological condition. The existence of this obstruction allows us to provide a systematic…
We consider the problem of computing $\ell$-page queue layouts, which are linear arrangements of vertices accompanied with an assignment of the edges to pages from one to $\ell$ that avoid the nesting of edges on any of the pages. Inspired…
The fitting problem for conjunctive queries (CQs) is the problem to construct a CQ that fits a given set of labeled data examples. When a fitting CQ exists, it is in general not unique. This leads us to proposing natural refinements of the…
A class of codimension one foliations has been recently introduced by imposing a natural compatibility condition with a closed maximally non-degenerate 2-form. In this paper we study for such foliations the information captured by a…
For any d-web by curves in an ambiant n-dimensional manifold, we define a tautological connection on some associated bundle, whose curvature vanishes iff the web has a maximal (n-1)-rank. As an application we recover, with the help of a…