Related papers: Stability data and t-structures on a triangulated …
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…
We recapture Douglas' framework for twisted parametrized stable homotopy theory in the language of $\infty$- categories. A twisted spectrum is essentially a section of a bundle of presentable stable $\infty$-categories whose fiber is the…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
This paper introduces a new algebraic notion - triangulated persistence category (TPC) - that refines that of triangulated category in the same sense that a persistence module is a refinement of the notion of a vector space. The spaces of…
This article deals with different generalizations of the discrete stability property. Three possible definitions of discrete stability are introduced, followed by a study of some particular cases of discrete stable distributions and their…
We establish some properties of the derived category of torus-equivariant coherent sheaves on a split toric stack bundle. Our main result is a semi-orthogonal decomposition of such a category.
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…
We interpret some results of persistent homology and barcodes (in any dimension) with the language of microlocal sheaf theory. For that purpose we study the derived category of sheaves on a real finite-dimensional vector space V. By using…
What is a time-varying graph, a time-varying topological space, or, more generally, a mathematical structure that evolves over time? In this work, we lay the foundations for a general theory of temporal data by introducing categories of…
We suggest a generalization of \pi_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of…
We propose an approach to study logarithmic sheaves T(-log A) associated with a hyperplane arrangements A on the projective space, based on projective duality, direct image functors and vector bundles methods. We focus on freeness of line…
We prove that a triangulated category which is the underlying category of a stable derivator has a filtered enhancement, providing an affirmative answer to a conjecture in [3].
In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…
We show that any bounded t-structure in the bounded derived category of a silting-discrete algebra is algebraic, i.e. has a length heart with finitely many simple objects. As a corollary, we obtain that the space of Bridgeland stability…
We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…
We classify (semi)stable sheaves on a rational curve with one node. The results are based on the classification of indecomposable torsion-free sheaves due to Drozd and Greuel "Tame and wild projective curves and classification of vector…
Generalized Navier-Stokes equations which were proposed recently to describe active turbulence in living fluids are analyzed rigorously. Results on wellposedness and stability in the $L^2(\mathbb{R}^n)$-setting are derived. Due to the…
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…
Roughly speaking, a conic bundle is a surface, fibered over a curve, such that the fibers are conics (not necessarily smooth). We define stability for conic bundles and construct a moduli space. We prove that (after fixing some invariants)…
Let $X$ be a finite-dimensional, noetherian scheme. Antieau, Gepner and Heller conjectured that its derived category of perfect complexes has a bounded t-structure if and only if $X$ is regular. We prove a generalization, and to do so we…