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In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a…
New criteria are shown that certain combinations of finite unimodal polynomials are unimodal. %Given unimodal polynomials with explicit expressions and dependent recursion relations, we propose an approach to determine their modes. As…
We show that the conditions imposed on a second order linear differential equation with rational coefficients on the complex line by requiring it to have regular singularities with fixed exponents at the points of a finite set $P$ and…
We consider the general question of how the homological finiteness property left-FPn holding in a monoid influences, and conversely depends on, the property holding in the substructures of that monoid. In particular we show that left-FPn is…
We study identities of finite dimensional algebras over a field of characteristic zero, graded by an arbitrary groupoid $\Gamma$. First we prove that its graded colength has a polynomially bounded growth. For any graded simple algebra $A$…
In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the curvature is integrable. Such points are called \emph{simple…
We characterise simply-connected biquotients which potentially admit metrics of holonomy G_2. We prove that there are at most three real homotopy types of rationally elliptic such manifolds---all of them being formal. In the course of this…
Assume that there exists a hypersurface singularity which cannot be resolved by iterated monoidal transformations in positive characteristic. We show that in the set of defining functions of hypersurface singularities which cannot be…
As shown by S. Eilenberg and J.C. Moore (1965), for a monad $F$ with right adjoint comonad $G$ on any catgeory $\mathbb{A}$, the category of unital $F$-modules $\mathbb{A}_F$ is isomorphic to the category of counital $G$-comodules…
In 1978 Durfee conjectured various inequalities between the signature and the geometric genus of a normal surface singularity. Since then a few counter examples have been found and positive results established in some special cases. We…
We introduce and develop the notion of "unipotent spectra." This is defined to be the stabilization of To\"en's category of affine stacks, and is related to recent work of Mondal--Reinecke. Unipotent spectra give rise to unipotent stable…
Stable equivalences of Morita type preserve many interesting properties and is proved to be the appropriate concept to study for equivalences between stable categories. Recently the singularity category attained much attraction and Xiao-Wu…
We present a systematic approach for achieving fairness in a binary classification setting. While we focus on two well-known quantitative definitions of fairness, our approach encompasses many other previously studied definitions as special…
In this sequel to Resolution except for minimal singularities I, we find the smallest class of singularities in four variables with which we necessarily end up if we resolve singularities except for normal crossings. The main new feature is…
We study equisingularity of families of reduced curves over smooth parameter spaces of arbitrary positive dimension, using the difference between two analytic invariants of a curve singularity: the multiplicity of its Jacobian ideal and its…
We study the connection between amenability, F{\o}lner conditions and the geometry of finitely generated semigroups. Using results of Klawe, we show that within an extremely broad class of semigroups (encompassing all groups, left…
We investigate mappings $F = (f_1, f_2) \colon \mathbb{R}^2 \to \mathbb{R}^2 $ where $ f_1, f_2 $ are bivariate normal densities from the perspective of singularity theory of mappings, motivated by the need to understand properties of…
Using polynomial interpolation, along with structural properties of the family of positive real rational functions, we here show that a set of m nodes in the open left half of the complex plane, can always be mapped to anywhere in the…
The weighted dual graph of a two-dimensional normal singularity $(X, x)$ represents the topological nature of the exceptional locus of its minimal log resolution. $(X, x)$ and its graph are said to be taut if the singularity can be uniquely…
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…