Joseph M. Landsberg

D-Index & Metrics D-index (Discipline H-index) only includes papers and citation values for an examined discipline in contrast to General H-index which accounts for publications across all disciplines.

Discipline name D-index Citations Publications World Ranking National Ranking
Mathematics D-index 32 Citations 4,364 179 World Ranking 2415 National Ranking 1024

Research.com Recognitions

Awards & Achievements

2017 - Fellow of the American Mathematical Society For contributions to differential geometry, geometry of projective varieties, representation theory, and complexity theory.

What is he best known for?

The fields of study he is best known for:

• Algebra
• Mathematical analysis
• Geometry

His primary scientific interests are in Algebra, Combinatorics, Secant variety, Rank and Conjecture. His work on Projective geometry, Function field of an algebraic variety, Algebraic geometry and Birational geometry as part of general Algebra study is frequently linked to Rational normal curve, therefore connecting diverse disciplines of science. Joseph M. Landsberg works mostly in the field of Algebraic geometry, limiting it down to concerns involving Matrix multiplication and, occasionally, Multilinear algebra.

His Combinatorics research is multidisciplinary, incorporating elements of Hypersurface, Upper and lower bounds and Multiplication. Joseph M. Landsberg works mostly in the field of Secant variety, limiting it down to topics relating to Representation theory and, in certain cases, Vector bundle, Tensor rank and State, as a part of the same area of interest. His Rank research incorporates themes from Symmetric tensor and Polynomial.

His most cited work include:

• Tensors: Geometry and Applications (505 citations)
• Cartan for beginners (206 citations)
• On the Ranks and Border Ranks of Symmetric Tensors (185 citations)

What are the main themes of his work throughout his whole career to date?

His scientific interests lie mostly in Pure mathematics, Combinatorics, Matrix multiplication, Rank and Algebra. His Pure mathematics study combines topics from a wide range of disciplines, such as Variety and Mathematical analysis. His Matrix multiplication study also includes

• Multiplication which connect with Operator,
• Space which is related to area like Geometric complexity theory.

His Rank research is multidisciplinary, incorporating perspectives in Discrete mathematics, Polynomial, Linear subspace and Symmetric tensor, Tensor. His study in the field of Representation theory, Function field of an algebraic variety and Secant variety is also linked to topics like Differential algebraic geometry. His Projective geometry study integrates concerns from other disciplines, such as Magic square and Freudenthal magic square.

He most often published in these fields:

• Pure mathematics (41.30%)
• Combinatorics (27.17%)
• Matrix multiplication (20.65%)

What were the highlights of his more recent work (between 2014-2021)?

• Matrix multiplication (20.65%)
• Combinatorics (27.17%)
• Rank (20.11%)

In recent papers he was focusing on the following fields of study:

His main research concerns Matrix multiplication, Combinatorics, Rank, Pure mathematics and Matrix. His Matrix multiplication study incorporates themes from Space, Algebraic geometry and Tensor. His Algebraic geometry research integrates issues from Numerical analysis and Representation theory.

His biological study spans a wide range of topics, including Symmetry, Upper and lower bounds and Symmetry group. His research in Rank intersects with topics in Computational complexity theory, Polynomial, Series and Tensor. His work in the fields of Pure mathematics, such as Projective geometry, overlaps with other areas such as Max-flow min-cut theorem, Periodic boundary conditions and Projective differential geometry.

Between 2014 and 2021, his most popular works were:

• New lower bounds for the border rank of matrix multiplication (51 citations)
• Geometric complexity theory: an introduction for geometers (36 citations)
• Geometry and Complexity Theory (30 citations)

In his most recent research, the most cited papers focused on:

• Mathematical analysis
• Algebra
• Geometry

Joseph M. Landsberg focuses on Matrix multiplication, Rank, Pure mathematics, Algebraic geometry and Tensor. His Matrix multiplication study combines topics in areas such as Upper and lower bounds, Tensor and Combinatorics. His research investigates the link between Rank and topics such as Multiplication that cross with problems in Algorithm and Hilbert scheme.

The various areas that Joseph M. Landsberg examines in his Pure mathematics study include Subvariety, Matrix algebra and Graph. The study incorporates disciplines such as Matrix, Numerical analysis and Representation theory in addition to Algebraic geometry. His research in Algebra is mostly concerned with Geometric complexity theory.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Tensors: Geometry and Applications

J. M. Landsberg.
(2011)

848 Citations

Tensors: Geometry and Applications

J. M. Landsberg.
(2011)

848 Citations

Cartan for beginners

Thomas Ivey;Joseph Landsberg.
(2003)

330 Citations

Cartan for beginners

Thomas Ivey;Joseph Landsberg.
(2003)

330 Citations

On the Ranks and Border Ranks of Symmetric Tensors

J. M. Landsberg;Zach Teitler.
Foundations of Computational Mathematics (2010)

232 Citations

On the Ranks and Border Ranks of Symmetric Tensors

J. M. Landsberg;Zach Teitler.
Foundations of Computational Mathematics (2010)

232 Citations

On the projective geometry of rational homogeneous varieties

Joseph M. Landsberg;Laurent Manivel.
Commentarii Mathematici Helvetici (2003)

189 Citations

On the projective geometry of rational homogeneous varieties

Joseph M. Landsberg;Laurent Manivel.
Commentarii Mathematici Helvetici (2003)

189 Citations

An Overview of Mathematical Issues Arising in the Geometric Complexity Theory Approach to $\mathbf{VP} eq\mathbf{VNP}$

Peter Bürgisser;J. M. Landsberg;Laurent Manivel;Jerzy Weyman.
SIAM Journal on Computing (2011)

145 Citations

On the Ideals of Secant Varieties of Segre Varieties

J. M. Landsberg;L. Manivel.
Foundations of Computational Mathematics (2004)

145 Citations

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