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The study of topological superconductivity is largely based on the analysis of simple mean-field models that do not conserve particle number. A major open question in the field is whether the remarkable properties of these mean-field models…
We introduce a general characterization of sudden cosmological singularities and investigate the classical stability of homogeneous and isotropic cosmological solutions of all curvatures containing these singularities to small scalar,…
We describe a new class of positive linear discrete-time switching systems for which the problems of stability or stabilizability can be resolved constructively. This class generalizes the class of systems with independently switching state…
We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal.…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
Several countries successfully use centralized matching schemes for school or higher education assignment, or for entry-level labour markets. In this paper we explore the computational aspects of a possible similar scheme for assigning…
We show that the number of parameters for CM-modules of prescribed rank is semi-continuous in families of CM rings of Krull dimension 1. This transfers a result of Knoerrer from the commutative to the not necessarily commutative case. For…
We show that many definitions of stability found in the learning theory literature are equivalent to one another. We distinguish between two families of definitions of stability: distribution-dependent and distribution-independent Bayesian…
Keisler proved that if $\theta$ is a strong limit cardinal and $\lambda$ is a singular cardinal, then the transfer relation $\theta\longrightarrow\lambda$ holds. In a previous paper, we studied initial elementary submodels of the…
We give the first (ZFC) dividing line in Keisler's order among the unstable theories, specifically among the simple unstable theories. That is, for any infinite cardinal $\lambda$ for which there is $\mu < \lambda \leq 2^\mu$, we construct…
This paper contributes to the theory of large cardinals beyond the Kunen inconsistency, or choiceless large cardinal axioms, in the context where the Axiom of Choice is not assumed. The first part of the paper investigates a periodicity…
In this paper, we study a stability transfer theorem in d-tame Metric Abstract Elementary classes, in a similar way as in [BaKuVa], but using superstability-like assumptions which involves a new independence notion (Tame Independence)…
We introduce a hierarchy of fast-growing complexity classes and show its suitability for completeness statements of many non elementary problems. This hierarchy allows the classification of many decision problems with a non-elementary…
We isolate a new large cardinal concept, "remarkability." Consistencywise, remarkable cardinals are between ineffable and omega-Erdos cardinals. They are characterized by the existence of "0^sharp-like" embeddings; however, they relativize…
We investigate, in ZFC, the behavior of abstract elementary classes (AECs) categorical in many successive small cardinals. We prove for example that a universal $\mathbb{L}_{\omega_1, \omega}$ sentence categorical on an end segment of…
Any Littlestone class, or stable graph, has finite sets which function as ``virtual elements'': these can be seen from the learning side as representing hypotheses which are expressible as weighted majority opinions of hypotheses in the…
We construct flux-stabilised IIB compactifications whose extra dimensions (EDs) have very different sizes, and use these to describe several vacua with a TeV string scale. Because we can access regimes where 2 dimensions are hierarchically…
We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An $(a,b)$-supermatch is a stable matching in which if $a$ pairs break up it is possible to find another stable…
We elaborate a scheme of trapping-expulsion management (TEM), in the form of the quadratic potential periodically switching between confinement and expulsion, as a means of stabilization of two-dimensional dynamical states against the…
The abstract boundary has, in recent years, proved a general and flexible way to define the singularities of space-time. In this approach an essential singularity is a non-regular boundary point of an embedding which is accessible by a…