Related papers: $F$-singularities: applications of characteristic …
This is a survey paper on the subject of strong uniqueness in approximation theory.
This article has the following aims: (1) Extend the notion of fuchsian singularities (of first kind) to base fields of arbitrary characteristic. (2) Discuss their relationship to mathematical objects of a different nature. (3) Provide a…
This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.
We present an application of elimination theory to the study of singularities over arbitrary fields, particularly to the open problem of resolution. A partial extension of a function, defining resolution of singularities over fields of…
This is a 20-year old review on singularities and singularity theorems. The main reason to submit it now is -apart from increasing its availability- to correct a very strange error that appears in the journal's online version: it contains…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
This is a survey on recent results regarding singularities that occur on higher dimensional stable varieties.
We give an essentially self-contained treatment of the fundamental analytic and algebraic features of regularity structures and its applications to the study of singular stochastic PDEs.
Fuchsian methods and their applications to the study of the structure of spacetime singularities are surveyed. The existence question for spacetimes with compact Cauchy horizons is discussed. After some basic facts concerning Fuchsian…
In this short survey article, we try to list maximum number of known results on class preserving automorphisms of finite $p$-groups. We conclude the survey with some interesting (at least for the author) open problems on this topic.
This is a survey paper on the quantitative analysis of the propagation of singularities for the viscosity solutions to Hamilton-Jacobi equations in the past decades. We also review further applications of the theory to various fields such…
We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.
In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.
We survey recent applications of topology and singularity theory in the study of the algebraic complexity of concrete optimization problems in applied algebraic geometry and algebraic statistics.
Approaches to automated grouping in singular spectrum analysis are considered. A new method for the identification of periodic components is proposed. The possibilities of extensions to multivariate time series and images are discussed.
This brief survey of some singularity invariants related to Milnor fibers should serve as a quick guide to references. We attempt to place things into a wide geometric context while leaving technicalities aside. We focus on relations among…
We introduce and study invariants of singularities in positive characteristic called F-thresholds. They give an analogue of the jumping coefficients of multiplier ideals in characteristic zero. We discuss the connection between the…
This article is an overview of the vanishing cycles method in number theory over function fields. We first explain how this works in detail in a toy example, and then give three examples which are relevant to current research. The focus…
This survey paper addresses uniqueness questions for symplectic forms on closed manifolds, explains what is known in several examples, and reviews some open problems.
This is a survey article on Hilbert-Kunz multiplicity and the F-signature.