Related papers: Singularities of stable varieties
We present a brief survey of fluctuations and large deviations of particle systems with subextensive growth of the variance. These are called hyperuniform (or superhomogeneous) systems. We then discuss the relation between hyperuniformity…
A stratified bundle is a vector bundle which is a D-module. We show that regular singularity of stratified bundles on smooth varieties in positive characteristic is preserved by pullback and that regular singularity can be checked on…
In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…
In this paper, we investigate the viability of cosmological models featuring a type II singularity that occurs during the past evolution of the Universe. We construct a scenario in which the singularity arises and then constrain the model…
The approach to the singularity in Gowdy spacetimes consists of velocity term dominated behavior, except at a set of isolated points. At and near these points, spiky features grow. This paper reviews what is known about these spikes.
This study reports on the evolution of the probability distribution in the configuration space of the two-dimensional Toda system. The distribution is characterized by singularities, which predominantly take two forms: double-cusped…
The majority of star formation results in binaries or higher multiple systems, and planets in such systems are constrained to a limited range of orbital parameters in order to remain stable against perturbations from stellar companions.…
In this paper we survey many of the known results about Morse boundaries and stability.
Several progresses have been done very recently on models for the dynamics of one or more vortex filaments in three-dimensional fluids. In this article we survey the recent and previous results in this topic. We also present some new…
Variational stability, in the sense of local good behavior of optimal values and solutions in problems of optimization under shifts in parameters, is important not only for validating model robustness in practical applications but also for…
In this talk we would like to review recent results on non-singular cosmological models. It has been recently shown that among stiff perfect fluid inhomogeneous spacetimes the absence of singularities is more common than it was expected in…
In this survey we discuss various aspects of the singularity invariants with differential origin derived from the $D$-module generated by $f^s$.
We investigate stability and dynamics of higher-order solitary waves in quadratic media, which have a central peak and one or more surrounding rings. We show existence of two qualitatively different behaviours. For positive phase mismatch…
We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by higher dimensional Tolman-Bondi space-time. The naked singularities are found to be gravitationally…
Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the…
Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities,…
We introduce a class of complex surface singularities - the blow-$ADE$ singularities - which are likely to be stable with respect to $\mu^*$-constant deformations. We prove such a stability property in several special cases. Here, we…
In this article, we investigate the stability of syzygy bundles corresponding to ample and globally generated vector bundles on smooth irreducible projective surfaces.
We investigate the presence of defect structures in generalized models described by real scalar field in $(1,1)$ space-time dimensions. We work with two distinct generalizations, one in the form of a product of functions of the field and…
We investigate singularities of all parallel surfaces to a given regular surface. In generic context, the types of singularities of parallel surfaces are cuspidal edge, swallowtail, cuspidal lips, cuspidal beaks, cuspidal butterfly and…