Related papers: Absolute desingularization in characteristic zero

The isomorphism of 0-homology groups of a categorical at zero semigroup and homology groups of its 0-reflector is proved. Some applications of 0-homology to Eilenberg-MacLane homology of semigroups are given.

We will present the benefits of using methods of non-standard analysis in dynamic projective geometry. One major application will be the desingulariazation of geometric constructions.

Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…

We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.

We compare some algebras appeared in the recent attempts to prove resolution of singularities in positive characteristic. We also construct an algebra which encodes the same information and it is equivalent, up to integral closure, to the…

Quasi-isometries are mappings on graphs, with distance-distortions parameterized by a multiplicative factor and an additive constant. The distance-distortions of quasi-isometries are in a general form that captures a wide range of…

Nuclear C*-algebras enjoy a number of approximation properties, most famously the completely positive approximation property. This was recently sharpened to arrange for the incoming maps to be sums of order-zero maps. We show that, in…

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.

A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…

An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a finite sequence of pairs, each one consiting of a sheaf of ideals and a positive…

We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are…

This paper is an overview of my recent work on abstract homomorphisms of algebraic groups. It is based on a talk given at the Conference on Group Actions and Applications in Geometry, Topology, and Analysis held in Kunming in July 2012.

Effective methods are introduced for testing zero-dimensionality of varieties at a point. The motivation of this paper is to compute and analyze deformations of isolated hypersurface singularities. As an application, methods for computing…

This is a survey on coarse geometry with an emphasis on coarse homology theories.

This paper seeks to prove the bijectivity of the "Nash mapping" from the set of irreducible components of the scheme parametrizing analytic arcs on an algebraic surface $X$ whose origin is a singular point, into the set of irreducible…

We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent…

In this paper, we propose two important extensions to cluster-weighted models (CWMs). First, we extend CWMs to have generalized cluster-weighted models (GCWMs) by allowing modeling of non-Gaussian distribution of the continuous covariates,…

A study of zero-dimensional theories, based on exact results, is presented. First, relying on a simple diagrammatic representation of the theory, equations involving the generating function of all connected Green's functions are…

This paper represents the main portion of the Ph.D. Thesis of the author, and is the first of the series of four papers, which is a joint work with K. Matsuki as a whole. We present a program toward constructing an algorithm for resolution…

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…