Related papers: Simple Homogeneous Models

Stable homotopy theory is governed by the principle that after inverting loop spaces, homotopy types become the representing objects for homology theories. We show that this principle extends to higher category theory: inverting…

We prove geometric and cohomological stabilization results for the universal smooth degree $d$ hypersurface section of a fixed smooth projective variety as $d$ goes to infinity. We show that relative configuration spaces of the universal…

Multiplicative and additive $D$-stability, diagonal stability, Schur $D$-stability, $H$-stability are classical concepts which arise in studying linear dynamical systems. We unify these types of stability, as well as many others, in one…

This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from…

The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…

Let $N$ be a normal subgroup of a group $G$. An $N$-module $Q$ is $G$-stable provided that $Q$ is equivalent to the twist $Q^g$ of $Q$ by $g$, for every $g\in G$. If the action of $N$ on $Q$ extends to an action of $G$ on $Q$, $Q$ is…

A brief introduction on the issue of stability in generalized modified gravity is presented and the dynamical system methods are used in the investigation of the stability of spatially flat homogeneous cosmologies within a large class of…

We extend the methods of geometric invariant theory to actions of non--reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non--reductive. Given a linearization of the natural action of…

In this paper, we exploit the theory of dense graph limits to provide a new framework to study the stability of graph partitioning methods, which we call structural consistency. Both stability under perturbation as well as asymptotic…

We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is…

This paper develops a process-based account of scientific explanation that reconceives grounding in terms of stabilisation. Grounding theories capture hierarchical dependence but lack criteria for when explanations remain adequate under…

A bar-joint framework $(G,p)$ is the combination of a finite simple graph $G=(V,E)$ and a placement $p:V\rightarrow \mathbb{R}^d$. The framework is rigid if the only edge-length preserving continuous motions of the vertices arise from…

A rich variety of amorphous solids are found in nature and technology, including ones formed via the vulcanization of long, flexible molecules. A special class -- those featuring a wide gap between the long timescales over which constraints…

We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…

Motivated by data on coauthorships in scientific publications, we analyze a team formation process that generalizes matching models and network formation models, allowing for overlapping teams of heterogeneous size. We apply different…

Representation stability is a theory describing a way in which a sequence of representations of different groups is related, and essentially contains a finite amount of information. Starting with Church-Ellenberg-Farb's theory of…

We study stable like behaviour in first order theories without the independence property. We introduce generically stable measures, give characterizatiions, and show their ubiquity. We also introduce generic compact domination. We also…

The homogeneous partly pinned fluid systems are simple models of a fluid confined in a disordered porous matrix obtained by arresting randomly chosen particles in a one-component bulk fluid or one of the two components of a binary mixture.…

This paper studies intermediate homogenization of inhomogeneous cosmological models. It shows that spherically symmetric models, regardless of the equation of state, can undergo intermediate homogenization, i.e. a model can approach a…

The independence complex of a graph G is a simplicial complex whose simplices are the independent sets in G. In the last couple of decades, the independence complexes of square grids (with various boundary conditions) have gained much…