HR job title
- Professor
- Contact Info
- 1 979 845 7554
Landsberg, Joseph Professor
Positions
- Professor, Mathematics, College of Arts and Sciences
My areas of research include:
1) Applications of algebraic geometry, differential geometry and representation theory to complexity theory,
2) Geometry of tensors and applications,
3) Exterior differential systems,
4) Geometry of projective varieties.
1) Applications of algebraic geometry, differential geometry and representation theory to complexity theory,
2) Geometry of tensors and applications,
3) Exterior differential systems,
4) Geometry of projective varieties.
- Overview
- Publications
- Research
- Teaching
- Works By Students
- Background
- Contact
- Other
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Overview
Publications
selected publications
-
academic article
-
Jelisiejew, J., Landsberg, J. M., & Pal, A.
(2023).
Concise tensors of minimal border rank. Mathematische Annalen.
abs/2205.05713, 1-45.
-
Huang, H., Landsberg, J. M., & Lu, J.
(2023).
GEOMETRY OF BACKFLOW TRANSFORMATION ANSATZE FOR QUANTUM MANY-BODY FERMIONIC WAVEFUNCTIONS. COMMUNICATIONS IN MATHEMATICAL SCIENCES.
21(5), 1447-1453.
-
Conner, A., Harper, A., & Landsberg, J. M.
(2023).
New lower bounds for matrix multiplication and $operatorname {det}_3$. 11.
-
Conner, A., Huang, H., & Landsberg, J. M.
(2022).
Bad and Good News for Strassen's Laser Method: Border Rank of Perm3 and Strict Submultiplicativity. Foundations of Computational Mathematics.
23(6), 2049-2087.
-
Geng, R., & Landsberg, J. M.
(2022).
On the geometry of geometric rank. 16(5), 1141-1160.
-
Landsberg, J. M.
(2022).
Algebraic geometry and representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science. 82, 101888-101888.
-
Conner, A., Gesmundo, F., Landsberg, J. M., & Ventura, E.
(2022).
RANK AND BORDER RANK OF KRONECKER POWERS OF TENSORS AND STRASSEN'S LASER METHOD. Computational Complexity.
31(1), 1-1.
-
Landsberg, J. M.
(2021).
Algebraic Geometry and Representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science. abs/2108.06263.
-
Geng, R., & Landsberg, J. M.
(2020).
On the geometry of geometric rank. 16, 1141-1160.
-
Conner, A., Huang, H., & Landsberg, J. M.
(2020).
Bad and good news for Strassen's laser method: Border rank of the 3x3 permanent and strict submultiplicativity. abs/2009.11391.
-
Conner, A., Harper, A., & Landsberg, J. M.
(2019).
New lower bounds for matrix multiplication and the 3x3 determinant. abs/1911.07981.
-
Conner, A., Gesmundo, F., Landsberg, J. M., & Ventura, E.
(2019).
Rank and border rank of Kronecker powers of tensors and Strassen's laser method. abs/1909.04785.
-
Conner, A., Gesmundo, F., Landsberg, J. M., & Ventura, E.
(2019).
Tensors with maximal symmetries. abs/1909.09518.
-
Ballard, G., Ikenmeyer, C., Landsberg, J. M., & Ryder, N.
(2019).
The geometry of rank decompositions of matrix multiplication II: 3 x 3 matrices. Journal of Pure and Applied Algebra.
223(8), 3205-3224.
-
Cardillo, M., Lombardini, L., Sparacino, V., Fiaschetti, P., & Filippetti, M.
(2019).
[Editorial]. Differential Geometry and Its Applications.
36(4), 1-1.
-
Chiantini, L., Ikenmeyer, C., Landsberg, J. M., & Ottaviani, G.
(2019).
The Geometry of Rank Decompositions of Matrix Multiplication I: 2 x 2 Matrices. Experimental Mathematics.
28(3), 322-327.
-
Chiantini, L., Ikenmeyer, C., Landsberg, J. M., & Ottaviani, G.
(2019).
The Geometry of Rank Decompositions of Matrix Multiplication I: 2 2 Matrices. 28, 322-327.
-
Landsberg, J. M., & Michaek, M.
(2019).
Towards finding hay in a haystack: explicit tensors of border rank greater than $2.02m$ in $C^motimes C^motimes C^m$. abs%2F1912.11927.
-
Gesmundo, F., & Landsberg, J. M.
(2019).
Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley. 15, 1-24.
-
Landsberg, J. M.
(2018).
The complexity of matrix multiplication: developments since 2014. Extended abstract of 2018 Oberwolfach Complexity meeting plenary lecture. abs/1811.11667.
-
Gesmundo, F., Landsberg, J. M., & Walter, M.
(2018).
Matrix product states and the quantum max-flow/min-cut conjectures. 59(10), 102205.
-
Landsberg, J. M., & Michalek, M.
(2018).
A 2n2 - log2(n)-1 Lower Bound for the Border Rank of Matrix Multiplication. 2018(15), 4722-4733.
-
Efremenko, K., Landsberg, J. M., Schenck, H., & Weyman, J.
(2018).
THE METHOD OF SHIFTED PARTIAL DERIVATIVES CANNOT SEPARATE THE PERMANENT FROM THE DETERMINANT. Mathematics of Computation.
87(312), 2037-2045.
-
Chiantini, L., Hauenstein, J. D., Ikenmeyer, C., Landsberg, J. M., & Ottaviani, G.
(2018).
Polynomials and the exponent of matrix multiplication. Bulletin of the London Mathematical Society.
50(3), 369-389.
-
Landsberg, J. M.
(2018).
On the Geometry of Matrix Multiplication. Notices of the American Mathematical Society.
65(04), 1-1.
-
Landsberg, J. M., Morse, J., Wickelgren, K., Kovcs, S. J., Shlyakhtenko, D., Frenkel, E., & Tosatti, V.
(2018).
AMS Spring Sectional Sampler. Notices of the American Mathematical Society.
65(04), 1-1.
-
Efremenko, K., Landsberg, J. M., Schenck, H., & Weyman, J.
(2018).
On minimal free resolutions of sub-permanents and other ideals arising in complexity theory. Journal of Algebra.
503, 8-20.
-
Landsberg, J. M., & Ryder, N.
(2017).
On the Geometry of Border Rank Algorithms for n x 2 by 2 x 2 Matrix Multiplication. Experimental Mathematics.
26(3), 275-286.
-
Landsberg, J. M., & Michalek, M.
(2017).
Abelian tensors. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES.
108(3), 333-371.
-
De Teran, F., Dopico, F. M., & Landsberg, J. M.
(2017).
An explicit description of the irreducible components of the set of matrix pencils with bounded normal rank. Linear Algebra and Its Applications.
520, 80-103.
-
Landsberg, J.
(2017).
Editorial. Differential Geometry and Its Applications.
55, 1-1.
-
Landsberg, J. M., & Ryder, N.
(2017).
On the Geometry of Border Rank Algorithms for n 2 by 2 2 Matrix Multiplication. 26, 275-286.
-
Ikenmeyer, C., & Landsberg, J. M.
(2017).
On the complexity of the permanent in various computational models. Journal of Pure and Applied Algebra.
221(12), 2911-2927.
-
Landsberg, J. M., & Ressayre, N.
(2017).
Permanent v. determinant: An exponential lower bound assuming symmetry and a potential path towards Valiant's conjecture. Differential Geometry and Its Applications.
55, 146-166.
-
Gesmundo, F., Hauenstein, J. D., Ikenmeyer, C., & Landsberg, J. M.
(2016).
Complexity of Linear Circuits and Geometry. Foundations of Computational Mathematics.
16(3), 599-635.
-
Landsberg, J. M., & Ottaviani, G.
(2015).
New lower bounds for the border rank of matrix multiplication. Theory of Computing.
11(1), 285-298.
-
Landsberg, J. M.
(2015).
Nontriviality of equations and explicit tensors in CmCmCm of border rank at least 2m2. Journal of Pure and Applied Algebra.
219(8), 3677-3684.
-
Landsberg, J. M.
(2015).
Geometric complexity theory: an introduction for geometers. Annali dell'Universita di Ferrara.
61(1), 65-117.
-
Kumar, S., & Landsberg, J. M.
(2015).
Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group. Discrete Mathematics.
338(7), 1232-1238.
-
Buczynski, J., & Landsberg, J. M.
(2014).
On the third secant variety. Journal of Algebraic Combinatorics: an international journal.
40(2), 475-502.
-
Kadish, H., & Landsberg, J. M.
(2014).
PADDED POLYNOMIALS, THEIR COUSINS, AND GEOMETRIC COMPLEXITY THEORY. Communications in Algebra.
42(5), 2171-2180.
-
Buczynski, J., Ginensky, A., & Landsberg, J. M.
(2013).
Determinantal equations for secant varieties and the Eisenbud-Koh-Stillman conjecture. Journal of London Mathematical Society.
88(1), 1-24.
-
Landsberg, J. M., & Ottaviani, G.
(2013).
Equations for secant varieties of Veronese and other varieties. Annali di Matematica Pura ed Applicata.
192(4), 569-606.
-
Landsberg, J. M., Manivel, L., & Ressayre, N.
(2013).
Hypersurfaces with degenerate duals and the Geometric Complexity Theory Program. Commentarii Mathematici Helvetici.
88(2), 469-484.
-
Hauenstein, J. D., Ikenmeyer, C., & Landsberg, J. M.
(2013).
Equations for Lower Bounds on Border Rank. Experimental Mathematics.
22(4), 372-383.
-
Landsberg, J. M., Morton, J., & Norine, S.
(2013).
Holographic algorithms without matchgates. Linear Algebra and Its Applications.
438(2), 782-795.
-
Buczynski, J., & Landsberg, J. M.
(2013).
Ranks of tensors and a generalization of secant varieties. Linear Algebra and Its Applications.
438(2), 668-689.
-
Landsberg, J. M., & Robles, C.
(2013).
Fubini-Griffiths-Harris Rigidity of Homogeneous Varieties. International mathematics research notices.
2013(7), 1643-1664.
-
Landsberg, J. M., Qi, Y., & Ye, K. e.
(2012).
ON THE GEOMETRY OF TENSOR NETWORK STATES. Quantum Information and Computation.
12(3-4), 346-354.
-
Landsberg, J. M., & Robles, C.
(2012).
FUBINI-GRIFFITHS-HARRIS RIGIDITY AND LIE ALGEBRA COHOMOLOGY. The Asian Journal of Mathematics.
16(4), 561-586.
-
Buergisser, P., Landsberg, J. M., Manivel, L., & Weyman, J.
(2011).
AN OVERVIEW OF MATHEMATICAL ISSUES ARISING IN THE GEOMETRIC COMPLEXITY THEORY APPROACH TO VP VNP. 40(4), 1179-1209.
-
Landsberg, J. M.
(2010).
P versus NP and geometry. 45(12), 1359-1377.
-
Landsberg, J. M., & Teitler, Z.
(2010).
On the Ranks and Border Ranks of Symmetric Tensors. Foundations of Computational Mathematics.
10(3), 339-366.
-
Landsberg, J. M., & Robles, C.
(2010).
Lines and osculating lines of hypersurfaces. Journal of London Mathematical Society.
82(3), 733-746.
-
Landsberg, J. M., & Tommasi, O.
(2010).
On the Debarre-de Jong and Beheshti-Starr Conjectures on Hypersurfaces with Too Many Lines. Michigan Mathematical Journal.
59(3), 573-588.
-
Landsberg, J. M., & Robles, C.
(2009).
Fubini's theorem in codimension two. Journal für die Reine und Angewandte Mathematik.
631(631), 221-235.
-
Landsberg, J. M., & Weyman, J.
(2009).
On secant varieties of compact Hermitian symmetric spaces. Journal of Pure and Applied Algebra.
213(11), 2075-2086.
-
Landsberg, J. M.
(2008).
Exterior differential systems, lie algebra cohomology, and the rigidity of homogenous varieties. Archivum Mathematicum.
44(5), 419-447.
-
Landsberg, J. M.
(2008).
Geometry and the complexity of matrix multiplication. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
45(2), 247-284.
-
Landsberg, J. M., & Manivel, L.
(2008).
Generalizations of Strassen's equations for secant varieties of Segre varieties. Communications in Algebra.
36(2), 405-422.
-
Landsberg, J. M., & Weyman, J.
(2007).
On the ideals and singularities of secant varieties of Segre varieties. Bulletin of the London Mathematical Society.
39(4), 685-697.
-
Landsberg, J. M., & Manivel, L.
(2007).
Legendrian varieties. The Asian Journal of Mathematics.
11(3), 341-359.
-
Landsberg, J. M., & Weyman, J.
(2007).
On tangential varieties of rational homogeneous varieties. Journal of London Mathematical Society.
76(2), 513-530.
-
Landsberg, J. M.
(2006).
The border rank of the multiplication of 2x2 matrices is seven. Journal of the American Mathematical Society.
19(2), 447-459.
-
Landsberg, J. M., & Manivel, L.
(2006).
The sextonions and E7 1/2. 201(1), 143-179.
-
Landsberg, J. M., & Manivel, L.
(2006).
A universal dimension formula for complex simple Lie algebras. Advances in Mathematics.
201(2), 379-407.
-
Landsberg, J. M.
(2006).
Griffiths-Harris rigidity of compact Hermitian symmetric spaces. Journal of Differential Geometry.
74(3), 395-405.
-
Landsberg, J. M., & Manivel, L.
(2004).
On the ideals of secant varieties of Segre varieties. Foundations of Computational Mathematics.
4(4), 397-422.
-
Fozunbal, M., McLaughlin, S. W., Schafer, R. W., & Landsberg, J. M.
(2004).
On space-time coding in the presence of spatio-temporal correlation. IEEE TRANSACTIONS ON INFORMATION THEORY.
50(9), 1910-1926.
-
Landsberg, J. M.
(2004).
On a conjecture of Kontsevich and variants of Castelnuovo's lemma (vol 115, pg 205, 1999). 140(4), 1112-1112.
-
Landsberg, J. M., & Manivel, L.
(2004).
Series of Lie groups. Michigan Mathematical Journal.
52(2), 453-479.
-
Landsberg, J. M., Manivel, L., & Westbury, B. W.
(2004).
Series of nilpotent orbits. Experimental Mathematics.
13(1), 13-29.
-
Landsberg, J. M., & Manivel, L.
(2003).
On the projective geometry of rational homogeneous varieties. Commentarii Mathematici Helvetici.
78(1), 65-100.
-
Landsberg, J. M.
(2003).
Lines on projective varieties. Journal für die Reine und Angewandte Mathematik.
562(562), 1-3.
-
Landsberg, J. M., & Manivel, L.
(2002).
Construction and classification of complex simple Lie algebras via projective geometry. Selecta Mathematica.
8(1), 137-159.
-
Landsberg, J. M., & Manivel, L.
(2002).
Triality, exceptional Lie algebras and Deligne dimension formulas. Advances in Mathematics.
171(1), 59-85.
-
Landsberg, J. M., & Manivel, L.
(2001).
The projective geometry of Freudenthal's magic square. Journal of Algebra.
239(2), 477-512.
-
Landsberg, J. M.
(1999).
On the infinitesimal rigidity of homogeneous varieties. 118(2), 189-201.
-
Landsberg, J. M.
(1999).
Is a linear space contained in a submanifold? On the number of derivatives needed to tell. Journal für die Reine und Angewandte Mathematik.
508(508), 53-60.
-
Landsberg, J. M.
(1999).
On a conjecture of Kontsevich and variants of Castelnuovo's lemma. Compositio Mathematica.
115(2), 231-239.
-
Ilic, B., & Landsberg, J. M.
(1999).
On symmetric degeneracy loci, spaces of symmetric matrices of constant rank and dual varieties. Mathematische Annalen.
314(1), 159-174.
-
Ivey, T., & Landsberg, J. M.
(1997).
On isometric and minimal isometric embeddings. DUKE MATHEMATICAL JOURNAL.
89(3), 555-576.
-
Landsberg, J. M.
(1996).
On degenerate secant and tangential varieties and local differential geometry. DUKE MATHEMATICAL JOURNAL.
85(3), 605-634.
-
Landsberg, J. M.
(1996).
Differential-geometric characterizations of complete intersections. Journal of Differential Geometry.
44(1), 32-73.
-
LANDSBERG, J. M.
(1994).
ON 2ND FUNDAMENTAL FORMS OF PROJECTIVE VARIETIES. Inventiones Mathematicae.
117(2), 303-315.
-
LANDSBERG, J. M.
(1992).
MINIMAL SUBMANIFOLDS DEFINED BY 1ST-ORDER SYSTEMS OF PDE. Journal of Differential Geometry.
36(2), 369-415.
-
Landsberg, J. M.
(1991).
Minimal submanifolds of E 2 n + 1 E^ {2n+1} arising from degenerate SO ( 3 ) extrm {SO} (3) orbits on the Grassmannian. Transactions of the American Mathematical Society.
325(1), 101-117.
-
Jelisiejew, J., Landsberg, J. M., & Pal, A.
(2023).
Concise tensors of minimal border rank. Mathematische Annalen.
abs/2205.05713, 1-45.
-
book
-
Landsberg, J. M.
(2017).
Geometry and Complexity Theory. Cambridge University Press (CUP).
-
Landsberg, J. M.
(2011).
Tensors Geometry and Applications. American Mathematical Soc..
-
Ivey, T., & Landsberg, J. M.
(2003).
Cartan for Beginners. Ed. 61.
American Mathematical Society (AMS).
-
Ivey, T. A., & Landsberg, J. M.
(2003).
Cartan for Beginners Differential Geometry Via Moving Frames and Exterior Differential Systems. American Mathematical Soc..
-
Landsberg, J. M.
(2017).
Geometry and Complexity Theory. Cambridge University Press (CUP).
-
conference paper
-
Conner, A., Landsberg, J. M., Gesmundo, F., & Ventura, E.
(2020).
Kronecker Powers of Tensors and Strassen's Laser Method. 10:1-10:1.
-
Malgouyres, F., & Landsberg, J.
(2016).
On the Identifiability and Stable Recovery of Deep/Multi-Layer Structured Matrix Factorization. 315-319.
-
Landsberg, J. M., & Ressayre, N.
(2016).
Permanent V. Determinant: An Exponential Lower Bound Assuming Symmetry. 29-35.
-
Conner, A., Landsberg, J. M., Gesmundo, F., & Ventura, E.
(2020).
Kronecker Powers of Tensors and Strassen's Laser Method. 10:1-10:1.
-
institutional repository document
-
Huang, H., & Landsberg, J. M.
(2023).
On Linear spaces of of matrices bounded rank
-
Landsberg, J. M., & Manivel, L.
(2022).
Equivariant spaces of matrices of constant rank
-
Landsberg, J. M.
(2022).
Secant varieties and the complexity of matrix multiplication
-
Jelisiejew, J., Landsberg, J. M., & Pal, A.
(2022).
Concise tensors of minimal border rank
-
Huang, H., Landsberg, J. M., & Lu, J.
(2021).
Geometry of backflow transformation ansatz for quantum many-body fermionic wavefunctions
-
Landsberg, J. M.
(2021).
Algebraic Geometry and Representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science
-
Geng, R., & Landsberg, J. M.
(2020).
On the geometry of geometric rank
-
Conner, A., Huang, H., & Landsberg, J. M.
(2020).
Bad and good news for Strassen's laser method: Border rank of the 3x3 permanent and strict submultiplicativity
-
Landsberg, J. M., & Michaek, M.
(2019).
Towards finding hay in a haystack: explicit tensors of border rank greater than $2.02m$ in $C^motimes C^motimes C^m$
-
Conner, A., Harper, A., & Landsberg, J. M.
(2019).
New lower bounds for matrix multiplication and the 3x3 determinant
-
Conner, A., Gesmundo, F., Landsberg, J. M., & Ventura, E.
(2019).
Rank and border rank of Kronecker powers of tensors and Strassen's laser method
-
Conner, A., Gesmundo, F., Landsberg, J. M., & Ventura, E.
(2019).
Tensors with maximal symmetries
-
Landsberg, J. M.
(2018).
The complexity of matrix multiplication: developments since 2014. Extended abstract of 2018 Oberwolfach Complexity meeting plenary lecture
-
Conner, A., Gesmundo, F., Landsberg, J. M., Ventura, E., & Wang, Y.
(2018).
Towards a Geometric Approach to Strassen's Asymptotic Rank Conjecture
-
Chiantini, L., Ikenmeyer, C., Landsberg, J. M., & Ottaviani, G.
(2016).
The geometry of rank decompositions of matrix multiplication I: 2x2 matrices
-
Ikenmeyer, C., & Landsberg, J. M.
(2016).
On the complexity of the permanent in various computational models
-
Efremenko, K., Landsberg, J. M., Schenck, H., & Weyman, J.
(2016).
The method of shifted partial derivatives cannot separate the permanent from the determinant
-
Landsberg, J. M., & Michaek, M.
(2016).
On the geometry of border rank algorithms for matrix multiplication and other tensors with symmetry
-
Landsberg, J. M., & Ryder, N.
(2015).
On the geometry of border rank algorithms for n x 2 by 2 x 2 matrix multiplication
-
Landsberg, J. M.
(2015).
An introduction to geometric complexity theory
-
Landsberg, J. M., & Ressayre, N.
(2015).
Permanent v. determinant: an exponential lower bound assumingsymmetry and a potential path towards Valiant's conjecture
-
Efremenko, K., Landsberg, J. M., Schenck, H., & Weyman, J.
(2015).
On minimal free resolutions of sub-permanents and other ideals arising in complexity theory
-
Landsberg, J. M., & Michaek, M.
(2015).
Abelian Tensors
-
Kumar, S., & Landsberg, J. M.
(2014).
Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group
-
Huang, H., & Landsberg, J. M.
(2023).
On Linear spaces of of matrices bounded rank
Research
principal investigator on
- AF: Small: Geometry and Complexity Theory awarded by National Science Foundation - (Arlington, Virginia, United States) 2018 - 2021
- Texas Geometry and Topology Conference (TGTC) awarded by National Science Foundation - (Arlington, Virginia, United States) 2018 - 2021
- Geometry and complexity theory awarded by National Science Foundation - (Arlington, Virginia, United States) 2015 - 2019
co-principal investigator on
Teaching
teaching activities
- MATH220 Foundations Of Math Instructor
- MATH411 Math Probability Instructor
- MATH423 Linear Algebra Ii Instructor
- MATH489 Sptp: Quantum Computing & Info Instructor
- MATH491 Hnr-research Instructor
- MATH620 Algebraic Geometry I Instructor
- MATH662 Seminar In Algebra Instructor
- MATH663 Seminar In Analysis Instructor
- MATH685 Directed Studies Instructor
- MATH689 Sptp: Algebraic Geometry Ii Instructor
- MATH689 Sptp: Quantum Comp & Info Instructor
- MATH689 Sptp:lie Groups And Algebras Instructor
- MATH691 Research Instructor
Works By Students
chaired theses and dissertations
-
Farnsworth, Cameron Lee (2016-05). The Polynomial Waring Problem and the Determinant.
-
Gesmundo, Fulvio (2017-04). Geometry and Representation Theory in the Study of Matrix Rigidity.
-
Guan, Yonghui (2016-05). Equations for Chow Varieties, Their Secant Varieties and Other Varieties Arising in Complexity Theory.
-
Liu, Bingjin (2016-04). Geometric Configurations of Algorithms for Reduced m x 2 and 2 x 2 Matrix Multiplication.
-
Porter, Curtis Wade (2016-06). The Local Equivalence Problem for 7-dimensional, 2-nondegenerate CR Manifolds whose Cubic Form is of Conformal Unitary Type.
-
Qi, Yang (2013-07). Geometry of Feasible Spaces of Tensors.
-
Yang, Ming 1984- (2012-09). On Partial and Generic Uniqueness of Block Term Tensor Decomposition in Signal Processing.
-
Ye, Ke (2012-10). Immanants, Tensor Network States and the Geometric Complexity Theory Program.
Background
education and training
awards and honors
- Fellow, conferred by American Mathematical Society - (Providence, Rhode Island, United States), 2017
Contact
first name
- Joseph
has last name
- Landsberg
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- jml@tamu.edu