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In this paper we extend To\"en's derived Hall algebra construction, in which he obtains unital associative algebras from certain stable model categories, to one in which such algebras are obtained from more general stable homotopy theories,…
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 distances on zigzag persistence modules from the viewpoint of derived categories and Auslander--Reiten quivers. The derived category of ordinary persistence modules is derived equivalent to that of arbitrary zigzag persistence…
In this paper homology stability for unitary groups over a ring with finite unitary stable rank is established. Homology stability of symplectic groups and orthogonal groups appears as a special case of our results.
The question of biological stability (permanence) of a replicator reaction-diffusion system is considered. Sufficient conditions of biological stability are found. It is proved that there are situations when biologically unstable…
Path equations of different orbiting objects in the presence of very strong gravitational fields are essential to examine the impact of its gravitational effect on the stability of each system. Implementing an analogous method, used to…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological…
Let A be the category of modules over a complex, finite-dimensional algebra. We show that the space of stability conditions on A parametrises an isomonodromic family of irregular connections on P^1 with values in the Hall algebra of A. The…
We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time orbital and asymptotic stability. We are…
This note revisits stability conditions on the bounded derived categories of coherent sheaves on irreducible projective curves. In particular, all stability conditions on smooth curves are classified and a connected component of the…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
Let $V$ be a complete discrete valuation ring with residue field $\mathbb{F}$. We define a cyclic homology theory for algebras over $\mathbb{F}$, by lifting them to free algebras over $V$, which we enlarge to tube algebras and complete…
We make a revision of the stability criteria for equatorial circular orbits, obtained from the epicyclic approximation, which is widely used in Newtonian models for axisymmetric galaxies. We find that, for the case of thin disk models, the…
We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact…
We study the space of stability conditions on $K3$ surfaces from the perspective of mirror symmetry. It is done in the so called attractor backgrounds (moduli) which can be far from the conventional large complex limits and are selected by…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
We classify connected finite acyclic graded quivers $Q$ for which the graded path algebra $kQ$, regarded as a formal dg algebra, is silting-discrete. We prove that $kQ$ is silting-discrete if and only if it is derived-discrete, and that…
We introduce a novel set of stability conditions for vacua with broken Lorentz symmetry. The first class of conditions require that the energy be minimized under small geometric deformations, which translates into requiring the positivity…