Related papers: Weighted Fundamental Group
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
We study the behaviour of the topological fundamental group under totally ramified abelian covers (a special case of abelian Galois covers) of complex projective varieties of dimension at least 2.
We study weight modules of the Lie algebra $W_2$ of vector fields on ${\mathbb C}^2$. A classification of all simple weight modules of $W_2$ with a uniformly bounded set of weight multiplicities is provided. To achieve this classification…
This article develops a practical technique for studying representations of $\Bbbk$-linear categories arising in the categorification of quantum groups. We work in terms of locally unital algebras which are $\mathbb{Z}$-graded with graded…
In this paper, as a step towards a unified mathematical treatment of the gauge functionals from quantum field theory that have found profound applications in mathematics, we generalize the Seiberg-Witten functional that in particular…
We propose and study a variation of the classical isomorphism problem for group rings in the context of projective representations. We formulate several weaker conditions following from our notion and give all logical connections between…
In this (partly expository) paper we show, using ideas from the theory of total positivity, how a number of properties of a semisimple group over the complex numbers can be presented purely in terms of the Weyl group. We also describe some…
The associahedron is an object that has been well studied and has numerous applications, particularly in the theory of operads, the study of non-crossing partitions, lattice theory and more recently in the study of cluster algebras. We…
Ehrenborg, Govindaiah, Park, and Readdy recently introduced the van der Waerden complex, a pure simplicial complex whose facets correspond to arithmetic progressions. Using techniques from combinatorial commutative algebra, we classify when…
Our earlier renormalization group analysis of simplicial gravity is extended. A high statistics study of the volume and coupling constant dependence of the cumulants of the node distribution is carried out. It appears that the phase…
This paper is dedicated to the study of weight complexes (defined on triangulated categories endowed with weight structures) and their applications. We introduce pure (co)homological functors that "ignore all non-zero weights"; these have a…
The number of nonisomorphic simplicial complexes with up to $n$ vertices increases super-exponentially with $n$, which makes exhaustive computation of invariants associated with such complexes a daunting task. In this paper we provide a…
In this paper we expand the theory of weighted sheaves over posets, and use it to study the local homology of Artin groups. First, we use such theory to relate the homology of classical braid groups with the homology of certain independence…
Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in…
We introduce the notion of a standard weighted graph and show that every weighted graph has an essentially unique standard model. Moreover we classify birational transformations between such models. Our central result shows that these are…
We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted…
The Seifert-van Kampen theorem computes the fundamental group of a space from the fundamental groups of its constituents. We develop a modular SVK framework within the setting of computational paths - an approach to equality where witnesses…
We present a thorough study of the differential geometry of weightings and develop the theory of weightings for vector bundles, Lie groupoids, and Lie algebroids. We begin by extending the work of Loizides and Meinrenken on weighted…
All simple weight modules with finite dimensional weight spaces over affine Lie algebras are classified.
Important decisions are likely made by groups of agents. Thus group decision making is very common in practice. Very transparent group aggregating rules are given by weighted voting, where each agent is assigned a weight. Here a proposal is…