相关论文: Singularities

Basic invariants of binary forms over $\mathbb C$ up to degree 6 (and lower degrees) were constructed by Clebsch and Bolza in the 19-th century using complicated symbolic calculations. Igusa extended this to algebraically closed fields of…

In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…

We sketch recent interactions between model theory and a roughly 150-year old study of analytic functions involving complex analysis, algebraic topology, and number theory, centered in canonicity of universal covers. Towards this goal we…

The first examples of exceptional terminal singularities are constructed.

We consider the class of curves of finite total curvature, as introduced by Milnor. This is a natural class for variational problems and geometric knot theory, and since it includes both smooth and polygonal curves, its study shows us…

This is the paper as published. The topology of a complex plane curve singularity with real branches is deduced from any real deformation having delta crossings. An example of the computation of the global geometric monodromy of a…

This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…

The familiar Bang/Crunch singularities of classical cosmology have recently been augmented by new varieties: rips, sudden singularities, and so on. These tend to be associated with final states. Here we consider an alternative possibility…

We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…

The paper contains a description of the links of complex surface germ.

The notion of cobordism of singular maps was introduced around 1980 by A. Sz\H{u}cs and U. Koschorke independently. As an application, Sz\H{u}cs used it to compute cobordism groups of immersions and embeddings in dimensions where the…

This is a largely expository paper about how groups arise or are of interest in model theory. Included are the following topics: classifying groups definable in specific structures or theories and the relation to algebraic groups, groups…

In this article we apply the results in the article "On Isolated Real Singularities I" to the study of real $ADE$-singularities. We show that said results enables us to find the homology groups of the Milnor fibres of real…

Numerical equivalence of algebraic cycles is defined abstractly by intersection numbers. Classically, for smooth complex proper toric varieties, the quotients by numerical equivalence with rational coefficients can be described…

The appearance of Marshall and Olkin's 1979 book on inequalities with special emphasis on majorization generated a surge of interest in potential applications of majorization and Schur convexity in a broad spectrum of fields. After 25 years…

This book consists of material originally appearing in the Problem Section of the journal Topology Proceedings since 1976 as well as some other well-known problem lists in general topology from the 1970's that have some connection to the…

Special relativity was discovered at the eve of the century, but finds its roots in the 19th century efforts to understand the optics and electromagnetism of moving bodies. These roots are reviewed in Parts 1 and 2, the latter being…

Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…

This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…

An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the…