Related papers: Desingularization in Computational Applications an…
We investigate the viability of defining an intersection product on algebraic cycles on a singular algebraic variety by pushing forward intersection products formed on a resolution of singularities. For varieties with resolutions having a…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
The study of hypersurfaces in a torus leads to the beautiful zoo of amoebas and their contours, whose possible configurations are seen from combinatorial data. There is a deep connection to the logarithmic Gauss map and its critical points.…
We present algorithmic and complexity results concerning computations with one and two real algebraic numbers, as well as real solving of univariate polynomials and bivariate polynomial systems with integer coefficients using Sturm-Habicht…
In this note we study the convergence of the survey decimation algorithm. An analytic formula for the reduction of the complexity during the decimation is derived. The limit of the converge of the algorithm are estimated in the random case:…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
This paper uses reconstruction algebras to construct simultaneous resolution of determinantal surfaces. The main new difference to the classical case is that, in addition to the quiver of the reconstruction algebra, certain noncommutative…
It is shown how one can apply the classification of the holonomy algebras of Lorentzian manifolds to solve some problems. In particular, a new proof to the classification of Lorentzian manifolds with recurrent curvature tensor is given; the…
Computational knot theory and 3-manifold topology have seen significant breakthroughs in recent years, despite the fact that many key algorithms have complexity bounds that are exponential or greater. In this setting, experimentation is…
Several problems in magnetically confined fusion, such as the computation of exterior vacuum fields or the decomposition of the total magnetic field into separate contributions from the plasma and the external sources, are best formulated…
Discontinuity with respect to data perturbations is common in algebraic computation where solutions are often highly sensitive. Such problems can be modeled as solving systems of equations at given data parameters. By appending auxiliary…
We study a set of topological roots of the local Bernstein-Sato polynomial of arbitrary plane curve singularities. These roots are characterized in terms of certain divisorial valuations and the numerical data of the minimal log resolution.…
We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and…
We give algorithms to construct the N\'eron Desingularization and the easy case from \cite{KK} of the General N\'eron Desingularization.
A short review of Algebraic Geometry tools for the decomposition of tensors and polynomials is given from the point of view of applications to quantum and atomic physics. Examples of application to assemblies of indistinguishable two-level…
We show how the Eulcidean algorithm for polynomials can be used to find the intersection points, with multiplicities, of two plane algebraic curves.
In this paper, we study residues of differential 2-forms on a smooth algebraic surface over an arbitrary field and give several statements about sums of residues. Afterwards, using these results we construct algebraic-geometric codes which…
Given a singular hypersurface in a regular 2-dimensional scheme essentially of finite type over a field, we construct an embedded resolution of singularities by weighted blow-ups. This differs from our earlier work which required…
We begin with modular form periods, a focal point of several Yuri Manin's works. The similarity is discussed between the corresponding zeta-polynomials and superpolynomials of algebraic links, closely related to Khovanov-Rozansky…