Related papers: Generalized stability for abstract homotopy theori…
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
We prove a new kind of homological stability theorem for automorphism groups of finitely-generated projective modules over Dedekind domains, which takes into account all possible stabilisation maps between these, rather than only…
We study projective functions. We prove that projective functions generalise lower and upper-semianalytic ones while being stable by composition and difference. We show that the class of projective functions is closed under sums,…
Without the axiom of choice, the free exact completion of the category of sets (i.e. the category of setoids) may not be complete or cocomplete. We will show that nevertheless, it can be enhanced to a derivator: the formal structure of…
Given a monoid defined by a presentation, and a homotopy base for the derivation graph associated to the presentation, and given an arbitrary subgroup of the monoid, we give a homotopy base (and presentation) for the subgroup. If the monoid…
This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…
We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasi-coherent modules on schemes,…
We investigate the standard stable manifold theorem in the context of a partially hyperbolic singu-larity of a vector field depending on a parameter. We prove some estimates on the size of the neighbourhood where the local stable manifold…
In this paper the following implication is verified for certain basic algebraic curves: if the additive real function $f$ approximately (i.e., with a bounded error) satisfies the derivation rule along the graph of the algebraic curve in…
We study the problem of existence and uniqueness of homotopy colimits in stable representation theory, where one typically does not have model category structures to guarantee that these homotopy colimits exist or have good properties. We…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
Affine Toda field theory with a pure imaginary coupling constant is a non-hermitian theory. Therefore the solutions of the equation of motion are complex. However, in $1+1$ dimensions it has many soliton solutions with remarkable…
We provide new $\infty$-categorical models for unstable and stable global homotopy theory. We use the notion of partially lax limits to formalize the idea that a global object is a collection of $G$-objects, one for each compact Lie group…
We investigate certain adjunctions in derived categories of equivariant spectra, including a right adjoint to fixed points, a right adjoint to pullback by an isometry of universes, and a chain of two right adjoints to geometric fixed…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
Diers developed a general theory of right multi-adjoint functors leading to a purely categorical, point-set construction of spectra. Situations of multiversal properties return sets of canonical solutions rather than a unique one. In the…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
In this article we establish two fundamental results for the sublevel set persistent homology for stationary processes indexed by the positive integers. The first is a strong law of large numbers for the persistence diagram (treated as a…
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…
This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the…