Related papers: Some remarks on formality in families

Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms.…

This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…

For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…

Let $\mathbb{K}$ be an algebraically closed field of characteristic 0. A finite dimensional Lie algebra $\mathfrak{g}$ over $\mathbb{K}$ is said to be stable if there exists a linear form $g\in\mathfrak{g}^{*}$ and a Zariski open subset in…

We prove the existence of Siegel disks with smooth boundaries in most families of holomorphic maps fixing the origin. The method can also yield other types of regularity conditions for the boundary. The family is required to have an…

Dynamic reliability block diagrams (DRBDs) are introduced to overcome the modeling limitations of traditional reliability block diagrams, such as the inability to capture redundant components. However, so far there is no algebraic framework…

We discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system - or a parameter dependent family - via the Poincar\'e Normal Form approach. We discuss this at first formally, and…

In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…

This document presents a simpler proof showcasing the NP-hardness of Familial Graph Compression.

This paper is dedicated to the study of the stability of multiplicities of group representations.

In this article I study the variation of Selmer groups in families of modular Galois representations that are congruent modulo a fixed prime $p \geq 5$. Motivated by analogies with Goldfeld's conjecture on ranks in quadratic twist families…

In this paper, we construct, for some $2$-groups $G$, explicit Galois extensions $E/\mathbb{Q}(T)$ of group $G$ with $E\cap\overline{\mathbb{Q}}=\mathbb{Q}$. We also provide explicit arithmetic progressions of integers $t_0$ such that the…

The focal point of this paper is to provide some simple and efficient criteria to judge the ${\cal D}$-stability of two families of polynomials, i.e., an interval multilinear polynomial matrix family and a polytopic polynomial family.…

We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of…

We characterize charmenability among arithmetic groups and deduce dichotomy statements pertaining normal subgroups, characters, dynamics, representations and associated operator algebras. We do this by studying the stationary dynamics on…

We study stability and bifurcations in holomorphic families of polynomial automorphisms of C^2. We say that such a family is weakly stable over some parameter domain if periodic orbits do not bifurcate there. We first show that this defines…

This is an addendum to a previous article, which aims to provide the proofs of some results in that paper (Theorem 7.5 and Proposition 9.15) which were removed from its final version. The reason for such omission is that these proofs follow…

We study a variant of algebraic K-theory and prove that it is stable and preserves module structures.

Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…

This is a survey on recent results regarding singularities that occur on higher dimensional stable varieties.