Related papers: Stability Conditions and Lagrangian Cobordisms
We study the relation between perverse stability conditions and geometric stability conditions under blow up. We confirm a conjecture of Toda in some special cases and show that geometric stability conditions can be induced from perverse…
We study symplectic Laplacians on compact symplectic manifolds with boundary. These Laplacians are associated with symplectic cohomologies of differential forms and can be of fourth-order. We introduce several natural boundary conditions on…
This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's notion of $\Pi$-stability. From a…
We describe spaces of Bridgeland stability conditions on certain triangulated categories associated to Coxeter systems. These categories are defined algebraically using the category of modules for zigzag algebras associated to Coxeter…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
This paper investigates the stability of different regions in the $(k,\gamma)$-plane for a class of fractional delay differential equations given by \begin{equation} D^{\alpha} x(t) = -\gamma x(t) + g\big(x(t - \tau_1)\big) - e^{-\gamma…
We explain how structures analogous to those appearing in the theory of stability conditions on abelian and triangulated categories arise in geometric invariant theory. This leads to an axiomatic notion of a central charge on a scheme with…
Let $X$ be a graded Liouville domain. Fix a pair of infinite loop spaces $\Psi = (\Theta \to \Phi)$ living over $(BO \to BU)$. This determines a spectral Fukaya category $\mathcal{F}(X;\Psi)$ whenever $TX$ lifts to $\Phi$, containing closed…
Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian submanifold of…
We prove that a stability condition on a K3 surface is determined by the masses of spherical objects up to a natural $\mathbb{C}$-action. This is motivated by the result of Huybrechts and the recent proposal of Bapat-Deopurkar-Licata on the…
We introduce $q$-stability conditions $(\sigma,s)$ on Calabi-Yau-$\mathbb{X}$ categories $\mathcal{D}_\mathbb{X}$, where $\sigma$ is a stability condition on $\mathcal{D}_\mathbb{X}$ and $s$ a complex number. We prove the corresponding…
We introduce the notion of relative stability conditions on triangulated categories with respect to left admissible subcategories, based on arXiv:math/0212237, and demonstrate the deformation of relative stability conditions via the…
We show that the conjectural construction proposed by Bayer, Bertram, Macr\'i and Toda gives rise to Bridgeland stability conditions for a principally polarized abelian three-fold with Picard rank one by proving that tilt stable objects…
Given a collection of exact Lagrangians in a Liouville manifold, we construct a map from the Hochschild homology of the Fukaya category that they generate to symplectic cohomology. Whenever the identity in symplectic cohomology lies in the…
Hybrid dynamical systems exhibit a diverse array of stability phenomena, each currently addressed by separate Lyapunov-like results. We show that these results are all instances of a single theorem: a Lyapunov function is a morphism from a…
We extend the method of controlled Lagrangians with kinetic shaping to those mechanical systems on semidirect product Lie groups with broken symmetry, more specifically to the Euler--Poincar\'e equations with advected parameters. We find a…
Let $\mathrm{h}\mathscr{C}$ be the homotopy category of a stable infinity category $\mathscr{C}$. Then the homotopy category $\mathrm{h}\mathscr{C}^{\Delta^{1}}$ of morphisms in the stable infinity category $\mathscr{C}$ is also…
We develop a framework relating semiorthogonal decompositions of a triangulated category $\mathcal{C}$ to paths in its space of stability conditions. We prove that when $\mathcal{C}$ is the homotopy category of a smooth and proper…
We study Lagrangian cobordism groups of oriented surfaces of genus greater than two. We compute the immersed oriented Lagrangian cobordism group of these surfaces. We show that a variant of this group, with relations given by unobstructed…
Let $X$ be a smooth compact complex surface with the canonical divisor $K_X$ ample and let $\Theta_X$ be its holomorphic tangent bundle. Bridgeland stability conditions are used to study the space $H^1 (\Theta_X)$ of infinitesimal…