Related papers: Stability conditions and the braid group
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
A class of partially wrapped Fukaya categories in $T^* N$ are proven to be well defined and then studied. In the case of $N$ diffeomorphic to $\mathbb{R}^m \times \mathbb{T}^n$, it is shown that these categories provide homological mirrors…
We consider a 3-Calabi-Yau triangulated category associated to an ideal triangulation of a marked bordered surface. Using the theory of harmonic maps between Riemann surfaces, we construct a natural map from a component of the space of…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
We study the stabilization of a twisted modulus in Type IIB flux compactifications on a mirror of the rigid Calabi-Yau threefold. By analyzing the effective action of twisted and untwisted moduli, we find that three-form fluxes satisfying…
We extend the notion of stability in the non-abelian category of poset representations (introduced by Futorny and Iusenko) to the category of socle-projective representations of a given $r$-peak poset $\P$. When $\P$ is a poset of type…
We investigate stability conditions related to the existence of solutions of the Hull-Strominger system with prescribed balanced class. We build on recent work by the authors, where the Hull-Strominger system is recasted using non-Hermitian…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…
We show that any extremal contraction from a smooth projective variety with dimension less than or equal to three appears as a moduli space of (semi)stable objects in the derived category of coherent sheaves.
We define a one-dimensional family of "Euler" stability conditions on $\mathbb{P}^n$ which are conjectured to converge to Gieseker stability for coherent sheaves. Here, we focus on ${\mathbb P}^3$, first identifying Euler stability…
We consider stable minimal surfaces of genus 1 in Euclidean space and in Riemannian manifolds. Under the condition of covering stability (all finite covers are stable) we show that a genus 1 finite total curvature minimal surface in…
We study conditions on the topological D-branes of types A and B obtained by requiring a proper matching of the spectral flow operators on the boundary. These conditions ensure space-time supersymmetry and stability of D-branes. In most…
Schwinger's algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids.…
We study dynamical moduli stabilization driven by gaugino condensation in supergravity. In the presence of background radiation, there exists a region of initial conditions leading to successful stabilization. We point out that most of the…
Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…
The derived category of coherent sheaves $\mathcal{T}_B$ associated to a birational cobordism which is either a weighted projective space, a stacky Atiyah flip, or a stacky blow-up of a point has a conjectural mirror Fukaya-Seidel category…
Many of the large structures of the cell, such as the cytoskeleton, are assembled and maintained far from equilibrium. We study the stabilities of various structures for a simple model of such a far-from-equilibrium organized assembly in…
It is shown that the consideration of the braneworld consistency conditions within the framework of bulk modified gravities allows for the existence of thick branes in the five- dimensional case with compact extra dimension. In studing the…
Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…