AROMATH - 2019 - Annual activity report

AROMATH

AROMATH - 2019

Project-Team Aromath

Team, Visitors, External Collaborators

Overall Objectives

Research Program

High order geometric modeling
Robust algebraic-geometric computation

Application Domains

Geometric modeling for Design and Manufacturing.
Geometric modeling for Numerical Simulation and Optimization

New Results

Truncated Normal Forms for Solving Polynomial Systems: Generalized and Efficient Algorithms
Implicit representations of high-codimension varieties
Saturation of Jacobian ideals: Some applications to nearly free curves, line arrangements and rational cuspidal plane curves
Matrix formulae for Resultants and Discriminants of Bivariate Tensor-product Polynomials
Implicitizing rational curves by the method of moving quadrics
Separation bounds for polynomial systems
Sparse polynomial interpolation: sparse recovery, super resolution, or Prony?
Computing minimal Gorenstein covers
Symmetry Preserving Interpolation
Skew-Symmetric Tensor Decomposition
On the maximal number of real embeddings of minimally rigid graphs in $ℝ^{2}$ , $ℝ^{3}$ and $𝕊^{2}$
Voronoï diagram of orthogonal polyhedra in two and three dimensions
Near-Neighbor Preserving Dimension Reduction for Doubling Subsets of $L_{1}$
On the cross-sectional distribution of portfolio returns
Enumerating the morphologies of non-degenerate Darboux cyclides
Anisotropic convolution surfaces
A non-iterative method for robustly computing the intersections between a line and a curve or surface
Cooperative Visual-Inertial Sensor Fusion: the Analytic Solution
Overlapping Multi-Patch Structures in Isogeometric Analysis
First Order Error Correction for Trimmed Quadrature in Isogeometric Analysis
Consistent discretization of higher-order interface models for thin layers and elastic material surfaces, enabled by isogeometric cut-cell methods
Design of Self-Supporting Surfaces with Isogeometric Analysis
Low-rank space-time decoupled isogeometric analysis for parabolic problems with varying coefficients

Bilateral Contracts and Grants with Industry

Bilateral Contracts with Industry

Partnerships and Cooperations

European Initiatives
International Initiatives
International Research Visitors

Dissemination

Promoting Scientific Activities
Teaching - Supervision - Juries
Popularization

Bibliography

Publications of the year

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Section: New Results

Skew-Symmetric Tensor Decomposition

Participant : Bernard Mourrain.

In [2], we introduce the “skew apolarity lemma" and we use it to give algorithms for the skew-symmetric rank and the decomposition of tensors in $\land^{d} V_{ℂ}$ with $d \leq 3$ and $dim V_{ℂ} \leq 8$ . New algorithms to compute the rank and a minimal decomposition of a tri-tensor are also presented.

This is a joint work with Enrique Arrondo (UCM - Universidad Complutense de Madrid, Spain), Alessandra Bernardi (Department of Mathematics, University of Trento, Italy) Pedro Macias Marques (Departamento de Matemática da Universidade de Évora, Spain).

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