Related papers: The vanishing neighbourhood of non-isolated singul…
The number of Morse points in a Morsification determines the topology of the Milnor fibre of a holomorphic function germ $f$ with isolated singularity. If $f$ has an arbitrary singular locus, then this nice relation to the Milnor fibre…
The aim of this article is to provide space level maps between configuration spaces of graphs that are predicted by algebraic manipulations of cellular chains. More explicitly, we consider edge contraction and half-edge deletion, and…
Convenient mixed functions with strongly non-degenerate Newton boundaries have Milnor fibrations, as the isolatedness of the singularity follows from the convenience. In this paper, we consider the Milnor fibration for non-convenient mixed…
A detailed proof is given of a theorem describing the centraliser of a transitive permutation group, with applications to automorphism groups of objects in various categories of maps, hypermaps, dessins, polytopes and covering spaces, where…
We present an expository overview of the monoidal structures in the category of linearly compact vector spaces. Bimonoids in this category are the natural duals of infinite-dimensional bialgebras. We classify the relations on words whose…
The monodromy of torus bundles associated to completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article we…
We establish a "second vanishing theorem" for local cohomology modules over regular rings of unramified mixed characteristic, which relates the connectedness of the spectrum of a ring with the vanishing of local cohomology. Applying this,…
The `deautonomisation' of an integrable mapping of the plane consists in treating the free parameters in the mapping as functions of the independent variable, the precise expressions of which are to be determined with the help of a suitable…
A linear system on a smooth complex algebraic surface gives rise to a family of smooth curves in the surface. Such a family has a topological monodromy representation valued in the mapping class group of a fiber. Extending arguments of…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
We consider the topology for a class of hypersurfaces with highly nonisolated singularites which arise as exceptional orbit varieties of a special class of prehomogeneous vector spaces, which are representations of linear algebraic groups…
This thesis studies moduli spaces of singular connections on 3-manifolds and manifolds with cylindrical ends. A Chern-Simons functional is defined for singular connections on 3-manifolds which are singular along a knot. The critical points…
We introduce a simple calculus, extending a variant of the Steenbrink spectrum, for describing Hodge-theoretic invariants of (smoothings of) isolated singularities with (relative) automorphisms. After computing these "eigenspectra" in the…
In the present paper MAPLE subroutines computing Milnor and Tyurina numbers of an isolated algebraic hypersurface singularity are presented and described in detail. They represents examples, and perhaps the first ones, of a MAPLE…
The aim of this paper is to provide a discussion on current directions of research involving typical singularities of 3D nonsmooth vector fields. A brief survey of known results is presented. The main purpose of this work is to describe the…
We study a relation between brick $n$-tuples of subspaces of a finite dimensional linear space, and irreducible $n$-tuples of subspaces of a finite dimensional Hilbert (unitary) space such that a linear combination, with positive…
We prove extensions of Milnor's theorem for germs with nonisolated singularity and use them to find new classes of genuine real analytic mappings $\psi$ with positive dimensional singular locus $\Sing \psi \subset \psi^{-1}(0)$, for which…
A mixed basis approach based on density functional theory is extended to one-dimensional(1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the…
We give a large class of examples of non-uniqueness for the phase retrieval problem in multidimensions. Our constructions are based on "oblique tensorization", where one-dimensional results are strongly used, and its generalizations towards…
The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…