Related papers: Singularities of stable varieties
We review recent results concerning general properties of higher dimensional black holes. The topics selected with particular focus are those concerning topology, symmetry, and uniqueness properties of asymptotically flat vacuum black holes…
This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
This article, based on the talk given by one of the authors at the Pierrettefest in Castro Urdiales in June 2008, is an overview of a number of recent results on the polar invariants of plane curve singularities.
The necessity and benefit of singular solutions in the study of physical systems is shown. By singular solutions we mean solutions that are not contained in the general solution of the system of equations that describes the dynamic system…
This paper proposes a stable volume and a stable volume variant, referred to as a stable sub-volume, for more reliable data analysis using persistent homology. In prior research, an optimal cycle and similar ideas have been proposed to…
We investigate the dynamics of cellular solidification patterns using three-dimensional phase-field simulations. The cells can organize into stable hexagonal patterns or exhibit unsteady evolutions. We identify the relevant secondary…
We study the size and regularity properties of level sets of continuous functions with bounded upper-scaled and lower-scaled oscillation.
These are notes for a graduate-level introductory course on singularity categories.
We explore several variations on the recently discovered phenomena of murmurations for elliptic curves and modular forms.
We demonstrate that, in contrast with what was previously believed, multi-hump solitary waves can be stable. By means of linear stability analysis and numerical simulations, we investigate the stability of two- and three-hump solitary waves…
Recent developments in supersymmetric unified theories are reviewed, with particular emphasis on supersymmetric grand unification and a brief discussion of recent ideas about extra dimensions.
We provide a systematic approach to stable central limit theorems for d-dimensional martingale difference arrays and martingale difference sequences. The conditions imposed are straightforward extensions of the univariate case.
A contact singularity is a normal singularity $(V,0)$ together with a holomorphic contact form $\eta$ on $V\backslash$ Sing $V$ in a neighbourhood of 0, i.e. $\eta\wedge (d\eta)^r$ has no zero, where dim $V=2r+1$. The main result of this…
We study typical wall singularity of codimension one for locally compact geodesically complete metric spaces with an upper curvature bound. We provide a geometric structure theorem of codimension one singularity, and a geometric…
We derive some more results on the nature of the singularities arising in the collapse of inhomogeneous dust spheres. (i) It is shown that there are future-pointing radial and non-radial time-like geodesics emerging from the singularity if…
We give a survey on some aspects of deformations of isolated singularities. In addition to the presentation of the general theory, we report on the question of the smoothability of a singularity and on relations between different…
There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a…
We introduce a new class of self-sustained states, which may exist as single solitons or form multisoliton clusters, in driven passive cylindrical microresonators. Remarkably, such states are stabilized by the radiation they emit, which…
A rigorous way to obtain sharp bounds for Stokes constants is introduced and illustrated on a concrete problem arising in applications.