What is he best known for?
The fields of study he is best known for:
- Algebra
- Geometry
- Mathematical analysis
Bernard Mourrain spends much of his time researching Algebra, Polynomial, Computation, Topology and Combinatorics.
The Polynomial study combines topics in areas such as Monomial, Discrete mathematics, Dual space and Differential operator.
His work in Computation addresses subjects such as Algebraic number, which are connected to disciplines such as Geometry, Trifocal tensor, Epipolar geometry and Algebraic relations.
Bernard Mourrain combines subjects such as Box spline, Basis function, Algebraic curve, Differentiable function and Piecewise with his study of Topology.
His Combinatorics research is multidisciplinary, incorporating elements of Hankel matrix and Symmetric tensor.
His Elementary symmetric polynomial research incorporates themes from Triple system and Ring of symmetric functions.
His most cited work include:
- Symmetric Tensors and Symmetric Tensor Rank (435 citations)
- On the geometry and algebra of the point and line correspondences between N images (213 citations)
- Decomposition of quantics in sums of powers of linear forms (201 citations)
What are the main themes of his work throughout his whole career to date?
Bernard Mourrain mainly focuses on Algebra, Polynomial, Pure mathematics, Discrete mathematics and Algebraic number.
His Polynomial research incorporates elements of Basis and Monomial, Combinatorics.
His Pure mathematics research is multidisciplinary, relying on both Ring, Spline and Rank.
Particularly relevant to Algebraic curve is his body of work in Discrete mathematics.
Bernard Mourrain works mostly in the field of Algebraic number, limiting it down to topics relating to Computation and, in certain cases, Theoretical computer science, as a part of the same area of interest.
His biological study deals with issues like Domain, which deal with fields such as Applied mathematics.
He most often published in these fields:
- Algebra (25.58%)
- Polynomial (23.64%)
- Pure mathematics (17.83%)
What were the highlights of his more recent work (between 2015-2021)?
- Pure mathematics (17.83%)
- Polynomial (23.64%)
- Applied mathematics (13.18%)
In recent papers he was focusing on the following fields of study:
His primary scientific interests are in Pure mathematics, Polynomial, Applied mathematics, Algebraic number and Algebra.
The concepts of his Pure mathematics study are interwoven with issues in Basis, Basis function, Polygon mesh and Rank.
His work deals with themes such as Discrete mathematics, Infimum and supremum, Quotient, Ring and Relaxation, which intersect with Polynomial.
His studies in Applied mathematics integrate themes in fields like Multiplicity, Relaxation, Inverse system, Isogeometric analysis and Newton's method.
Bernard Mourrain has researched Algebraic number in several fields, including Intersection, Semidefinite programming, Interpolation, Noise and Restricted isometry property.
His Algebra research is multidisciplinary, incorporating perspectives in Cylinder and Polyhedron.
Between 2015 and 2021, his most popular works were:
- Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization (57 citations)
- Dimension and bases for geometrically continuous splines on surfaces of arbitrary topology (39 citations)
- $G^1$-smooth splines on quad meshes with 4-split macro-patch elements (21 citations)
In his most recent research, the most cited papers focused on:
- Algebra
- Geometry
- Mathematical analysis
His main research concerns Pure mathematics, Polynomial, Basis function, Spline and Rank.
His work focuses on many connections between Pure mathematics and other disciplines, such as Ring, that overlap with his field of interest in Matrix, Affine transformation and Ideal.
To a larger extent, Bernard Mourrain studies Algebra with the aim of understanding Polynomial.
The various areas that he examines in his Algebra study include Generalization and Truncated normal distribution.
His studies deal with areas such as Differentiable function, Piecewise and Topology as well as Spline.
His work carried out in the field of Rank brings together such families of science as Elimination theory, Tensor decomposition, Variety and Joins.
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