J. M. Landsberg

Found. Comput. Math., December, 2023

On Linear spaces of of matrices bounded rank.

[BibT_eX]

[DOI]

Hang Huang

CoRR, 2023

2022

Concise tensors of minimal border rank.

[BibT_eX]

[DOI]

Joachim Jelisiejew

Arpan Pal

CoRR, 2022

Rank and border rank of Kronecker powers of tensors and Strassen's laser method.

[BibT_eX]

[DOI]

Comput. Complex., 2022

2021

Algebraic Geometry and Representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science.

[BibT_eX]

[DOI]

CoRR, 2021

2020

On the geometry of geometric rank.

[BibT_eX]

[DOI]

Runshi Geng

CoRR, 2020

Bad and good news for Strassen's laser method: Border rank of the 3x3 permanent and strict submultiplicativity.

[BibT_eX]

[DOI]

Austin Conner

Hang Huang

CoRR, 2020

Kronecker Powers of Tensors and Strassen's Laser Method.

[BibT_eX]

[DOI]

Proceedings of the 11th Innovations in Theoretical Computer Science Conference, 2020

2019

Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley.

[BibT_eX]

[DOI]

Fulvio Gesmundo

Theory Comput., 2019

The Geometry of Rank Decompositions of Matrix Multiplication I: 2 × 2 Matrices.

[BibT_eX]

[DOI]

Exp. Math., 2019

Towards finding hay in a haystack: explicit tensors of border rank greater than 2.02m in Cm ⊗ Cm ⊗ Cm.

[BibT_eX]

[DOI]

CoRR, 2019

New lower bounds for matrix multiplication and the 3x3 determinant.

[BibT_eX]

[DOI]

Austin Conner

Alicia Harper

CoRR, 2019

Tensors with maximal symmetries.

[BibT_eX]

[DOI]

CoRR, 2019

2018

The method of shifted partial derivatives cannot separate the permanent from the determinant.

[BibT_eX]

[DOI]

Math. Comput., 2018

The complexity of matrix multiplication: developments since 2014. Extended abstract of 2018 Oberwolfach Complexity meeting plenary lecture.

[BibT_eX]

[DOI]

CoRR, 2018

A geometric study of Strassen's asymptotic rank conjecture and its variants.

[BibT_eX]

[DOI]

CoRR, 2018

The geometry of rank decompositions of matrix multiplication II: 3×3 matrices.

[BibT_eX]

[DOI]

CoRR, 2018

2017

On the Geometry of Border Rank Decompositions for Matrix Multiplication and Other Tensors with Symmetry.

[BibT_eX]

[DOI]

SIAM J. Appl. Algebra Geom., 2017

On the Geometry of Border Rank Algorithms for n × 2 by 2 × 2 Matrix Multiplication.

[BibT_eX]

[DOI]

Nicholas Ryder

Exp. Math., 2017

2016

Complexity of Linear Circuits and Geometry.

[BibT_eX]

[DOI]

Fulvio Gesmundo

Jonathan D. Hauenstein

Found. Comput. Math., 2016

A $2n^2-log(n)-1$ lower bound for the border rank of matrix multiplication.

[BibT_eX]

[DOI]

CoRR, 2016

On the geometry of border rank algorithms for matrix multiplication and other tensors with symmetry.

[BibT_eX]

[DOI]

CoRR, 2016

On the complexity of the permanent in various computational models.

[BibT_eX]

[DOI]

CoRR, 2016

The geometry of rank decompositions of matrix multiplication I: 2x2 matrices.

[BibT_eX]

[DOI]

CoRR, 2016

Permanent v. Determinant: An Exponential Lower Bound Assuming Symmetry.

[BibT_eX]

[DOI]

Nicolas Ressayre

Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, 2016

2015

New Lower Bounds for the Border Rank of Matrix Multiplication.

[BibT_eX]

[DOI]

Giorgio Ottaviani

Theory Comput., 2015

Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group.

[BibT_eX]

[DOI]

Shrawan Kumar

Discret. Math., 2015

On the geometry of border rank algorithms for n x 2 by 2 x 2 matrix multiplication.

[BibT_eX]

[DOI]

Nicholas Ryder

CoRR, 2015

Permanent v. determinant: an exponential lower bound assumingsymmetry and a potential path towards Valiant's conjecture.

[BibT_eX]

[DOI]

Nicolas Ressayre

CoRR, 2015

Abelian Tensors.

[BibT_eX]

[DOI]

CoRR, 2015

An introduction to geometric complexity theory.

[BibT_eX]

[DOI]

CoRR, 2015

On minimal free resolutions and the method of shifted partial derivatives in complexity theory.

[BibT_eX]

[DOI]

CoRR, 2015

2014

New Lower Bounds for the Rank of Matrix Multiplication.

[BibT_eX]

[DOI]

SIAM J. Comput., 2014

2013

Determinantal equations for secant varieties and the Eisenbud-Koh-Stillman conjecture.

[BibT_eX]

[DOI]

Jaroslaw Buczynski

Adam Ginensky

J. Lond. Math. Soc., 2013

Equations for Lower Bounds on Border Rank.

[BibT_eX]

[DOI]

Jonathan D. Hauenstein

Exp. Math., 2013

Computer aided methods for lower bounds on the border rank

[BibT_eX]

[DOI]

Jonathan D. Hauenstein

CoRR, 2013

Geometric Complexity Theory: an introduction for geometers.

[BibT_eX]

[DOI]

CoRR, 2013

2012

Explicit tensors of border rank at least 2n-1

[BibT_eX]

[DOI]

CoRR, 2012

Padded polynomials, their cousins, and geometric complexity theory

[BibT_eX]

[DOI]

Harlan Kadish

CoRR, 2012

2011

An Overview of Mathematical Issues Arising in the Geometric Complexity Theory Approach to VP≠VNP.

[BibT_eX]

[DOI]

SIAM J. Comput., 2011

2010

P versus NP and geometry.

[BibT_eX]

[DOI]

J. Symb. Comput., 2010

On the Ranks and Border Ranks of Symmetric Tensors.

[BibT_eX]

[DOI]

Zach Teitler

Found. Comput. Math., 2010

Hypersurfaces with degenerate duals and the Geometric Complexity Theory Program

[BibT_eX]

[DOI]

Laurent Manivel

Nicolas Ressayre

CoRR, 2010

2009

An overview of mathematical issues arising in the Geometric complexity theory approach to VP v.s. VNP

[BibT_eX]

[DOI]

CoRR, 2009

Holographic algorithms without matchgates

[BibT_eX]

[DOI]

Jason Morton

Serguei Norine

CoRR, 2009

2007

Geometry and the complexity of matrix multiplication

[BibT_eX]

[DOI]

CoRR, 2007

2004

On Space-Time Coding in the Presence of Spatio-Temporal Correlation.

[BibT_eX]

[DOI]

IEEE Trans. Inf. Theory, 2004

On the Ideals of Secant Varieties of Segre Varieties.

[BibT_eX]

[DOI]

Laurent Manivel

Found. Comput. Math., 2004

Series of Nilpotent Orbits.

[BibT_eX]

[DOI]