Related papers: Spanning subspace configurations and representatio…

In this paper, we study the topology of ordered Hurwitz space. These are moduli spaces of branched covers with a choice of ordering on the branched points. Answering a question of Ellenberg, we prove that the homology of ordered Hurwitz…

Existing methods rarely capture the temporal evolution of solution norms in vector nonlinear DDEs with variable delays and coefficients, often leading to overly conservative boundedness and stability criteria. We develop a framework that…

In this paper we present a new proof of the homological stability of the moduli space of closed surfaces in a simply connected background space $K$, which we denote by $S_g (K)$. The homology stability of surfaces in $K$ with an arbitrary…

Let $C$ be a curve of genus $g\geq 2$. A coherent system on $C$ consists of a pair $(E,V)$ where $E$ is an algebraic vector bundle of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of sections of $E$. The stability of the…

In this article, we extend an argument of Vogtmann in order to show homology stability of the Euclidean orthogonal group $O_n(A)$ when $A$ is a valuation ring subject to arithmetic conditions on either its residue or its quotient field. In…

We investigate the stability of persistence diagrams \( D \) under non-uniform scaling transformations \( S \) in \( \mathbb{R}^n \). Given a finite metric space \( X \subset \mathbb{R}^n \) with Euclidean distance \( d_X \), and scaling…

Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…

In this paper homology stability for unitary groups over a ring with finite unitary stable rank is established. Homology stability of symplectic groups and orthogonal groups appears as a special case of our results.

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

For a random variable $N = 0, 1, 2, \ldots$ we study the following question: When does the sum of $N$ many independent and identically distributed copies of a random variable $X$ have the same law a a nontrivial rescaling of $X$? We show…

A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$,…

In this paper we present a method for considering the stability of smooth vector fields on a smooth manifold which may not be compact. We show that these kind of stability which is called "connection stability" is equivalent to the…

We explicitly study the extremal stability of configuration spaces of complex projective spaces of any dimension, and show that the homology groups are vanish in extremal stable range. As a consequence, we give an affirmative answer of the…

Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…

We provide a uniform approach to obtain sufficient criteria for a (higher order) fixed point of a given bracket structure on a manifold to be stable under deformations. Examples of bracket structures include Lie algebroids, Lie…

We present a method which provides a unified framework for most stability theorems that have been proved in graph and hypergraph theory. Our main result reduces stability for a large class of hypergraph problems to the simpler question of…

This paper continues the study of the poset of eigenspaces of elements of a unitary reflection group (for a fixed eigenvalue), which was commenced in [6] and [5]. The emphasis in this paper is on the representation theory of unitary…

We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…

We use a recently proposed formulation of stable holomorphic vector bundles $V$ on elliptically fibered Calabi--Yau n-fold $Z_n$ in terms of toric geometry to describe stability conditions on $V$. Using the toric map $f: W_{n+1} \to…

We present a general framework how to investigate stability of solutions within a single self-consistent renormalization scheme being a parquet-type extension of the Baym-Kadanoff construction of conserving approximations. To obtain a…