**Office: Blocker 601H**

Office hours: by appointment in summer

**E-mail: **jml@math.tamu.edu

TAMU math dept homepage

Supported by NSF grant CCF-1814254

Spring 2021: Clay Senior Scholar at IPAM (remote)

Fall 2021: Graduate course on Representation Theory of Lie groups and algebras

Math 689 meeting MWF 10-11am

Spring 2022: Chaire d'excellence (visiting endowed professorship) U. Toulouse

I organize and co-organize:

Geometry seminar, meeting Mondays 3-4pm Bloc 220 and Fridays 4-5pm on zoom.

Working seminar for post-docs and graduate students meeting Wed. 10-11

RANDOM TENSORS (joint with G. Paouris) Meeting ??

What is representation theory? starting fall 2021 (an expositiory seminar), meeting Thursdays 11-12

Everyone is welcome to the seminars, graduate students

are particularly encouraged to attend.

TAMU seminar calendar

My CV (last updated 1/21)

Brief biographical sketch (updated 8/19)

My travel plans on hold

I am on the editorial board of Foundation of Computational Mathematics, Differential Geometry and its Applications, SIGMA, and Linear Algebra and its Applications. DGA has expanded its scope to include articles on applications of geometry to complexity theory.

PAPERS/PREPRINTS since 2013

- On the geometry of geometric rank (with R. Geng)
- Bad and Good news for Strassen's laser method: Border rank of the 3x3 permanent and strict submultiplicativity (with A. Conner and H. Huang) supplementary files
- Towards finding hay in a haystack: explicit tensors of border rank greater than (2.02)m in C^m \otimes C^m\otimes C^m (with M. Michalek)
- New lower bounds for matrix multiplication and det_3 (with A. Conner and A. Harper) supplementary files.
- Tensors with maximal symmetries (with A. Conner, F. Gesmundo, and E. Ventura)
- Kronecker powers of tensors useful for Strassen's laser method (with A. Conner, F. Gesmundo, and E. Ventura) supplementary files
- A geometric study of Strassen's asymptotic rank conjecture and its variants (with A. Conner, F. Gesmundo, E. Ventura and Y. Wang), Collectanea
- Matrix Product States and the Quantum Max-Flow/Min-Cut Conjectures (with F. Gesmundo and M. Walter, J. Mathematical Physics 2018)
- The geometry of rank decompositions of matrix multiplication II: 3x3 matrices (with G. Ballard, C. Ikenmeyer, and N. Ryder, JPAA 2018)
- Polynomials and the exponent of matrix multiplication (with L. Chiantini, J. Hauenstein, C. Ikenmeyer, and G. Ottaviani, Bull. LMS 2018)
- Explicit polynomial sequences with maximal spaces of partial derivatives and a question of K. Mulmuley (with F. Gesmundo, Theory of Computing 2019)
- Stable recovery of the factors from a deep matrix product and application to convolutional network (with F. Malgouyres), SIAM J. MATH. DATA SCI.
- The geometry of rank decompositionsof matrix multiplication I: 2x2 matrices (with L. Chiantini, C. Ikenmeyer and G. Ottaviani, Exper. Math)
- On the complexity of the permanent in various computational modes (with C. Ikenmeyer, JPAA 2017) ancillary files for the computational models paper: 6x6, 7x7, 8x8, 9x9
- Shifted partial derivatives cannot separate the permanent from the determinant (with K. Efremenko, H. Schenck, and J. Weyman, MOCM 2018)
- A 2n^2-log_2(n)-1 lower bound for the border rank of matrix multiplication (with M. Michalek, IMRN 2018)
- An explicit description of the irreducible components of the set of matrix pencils with bounded normal rank (with F. De Teran and F. Dopico, LAA,2017)
- On the geometry of border rank algorithms for matrix multiplication and other tensors with symmetry (with M. Michalek, SIAGA 2017)
- On the geometry of border rank algorithms for n x 2 by 2 x 2 matrix multiplication (with N. Ryder, Exper. Math. 2017)
- Permanent vs determinant: an exponential lower bound assuming symmetry and a potential path towards Valiant's conjecture (with N. Ressayre, DGA special issue on geometry and complexity 2017)
- ON MINIMAL FREE RESOLUTIONS OF SUB-PERMANENTS AND OTHER IDEALS ARISING IN COMPLEXITY THEORY (with K. Efremenko, H. Schenck and J. Weyman, Jalg 2018)
- papers 2013-2018

Survey articles

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

A very brief introduction to quantum computing and quantum information theory for mathematicians

An introduction to Geometric Complexity Theory (Newsletter of the EMS 3/16)

Exterior differential systems, Lie algebra cohomology, and the rigidity of homogeneous varieties (2008)

Differential geometry of submanifolds of projective space (2006)

Exterior differential systems and billiards (2006)

Representation theory and projective geometry (with L. Manivel), 2004

Books:

Quantum Computation and Information: a mathematical introduction

draft copy available upon request here is the table of contents

## Tensors: Asymptotic Geometry and Developments 2016–2018

Geometry and complexity theory: Cambridge University Press studies in advanced mathematics 169. Click here to see a draft copyCBMS Regional Conference Series in MathematicsVol:132

Tensors: Geometry and Applications.

AMS GSM 128. Click here for corrections and additions

Cartan For Beginners: Differential geometry via moving framesand exterior differential systems,(with T. Ivey) AMS GSM 175

Second Edition

Slides of recent talks:

IPAM lectures 2021: tutorial 1, tutorial 2, clay lecture 1, clay lecture 2, clay lecture 3

Efficient matrix multiplication (ILAS, Rio de Janiero, 7/19)

On The geometry of matrix multiplication (AMS sectional, Vanderbilt 4/18)

Symmetry versus Optimality (SIAM-AG, Atlanta 7/17)

Complexity theory and geometry (Berlin Mathematical School colloquium 2/15)

Perm v. det: an exponential lower bound assuming symmetry (Innovations in Theoretical Computer Science 1/16)

math reviews of all published papers

PhD students:

Current students: Chia-Yu Chang, Runshi Geng, and Arpan Pal

Graduated students:

Kashif Bari, May 2021, On the structure tensor of sl_n

Austin Conner, May 2020 New results in the complexity of matrix multiplication,

currently NSF postdoctoral fellow at Harvard University

Fulvio Gesmundo, May 2017, Geometry and representation theory in the study of matrix rigidity

currently post-doctoral fellow at U. Copenhagen

Cameron Farnsworth, August 2016, THE POLYNOMIAL WARING PROBLEM AND THE DETERMINANT

Post-doctoral fellow at Yongsei Univ. (Seoul), currently U. Texas San Marcos

Yonghui Guan, August 2016, EQUATIONS FOR CHOW VARIETIES, THEIR SECANT VARIETIES AND

OTHER VARIETIES ARISING IN COMPLEXITY THEORY

currently Computer Vision Algorithm Scientist at MINIEYE in Shenzhen China.

Curtis Porter, August 2016 THE LOCAL EQUIVALENCE PROBLEM FOR 7-DIMENSIONAL, 2-NONDEGENERATE CR

MANIFOLDS WHOSE CUBIC FORM IS OF CONFORMAL UNITARY TYPE,

Post-doctoral fellow at NC State Univ. Currently U. Hradec Kralove (Czech Republic)

Yang Qi, PhD August 2013 Geometry of Feasible Spaces of Tensors

determined defining equations for the third secant variety of a triple Segre product and closedness of tensor network states,

currently post-doctoral fellow at U. Chicago.

Ke Ye, PhD August 2012, IMMANANTS, TENSOR NETWORK STATES AND THE GEOMETRIC

COMPLEXITY THEORY PROGRAM determined symmetry groups of immanents, and closedness of tensor network states,

obtained Dickenson postdoctoral fellowship at U. Chicago, currently tenure track at Chinese Academy of Science.

Ming Yang, PhD Sept. 2012,On partial and generic uniqueness of block term tensor decompositions in signal processing, solving questions originating in signal processing. Currently Assistant Professor, Data Science - Westfield State University

Luke Oeding, PhD May 2009, Defining equations of the varietyof principal minors solved a conjecture of Holtz and Sturmfels.

NSF international postdoctoral fellow (Florence), UC Berkeley post-doc, currently tenure track at Auburn U.

Frederic Holweck, PhD fall 04, Dual varieties, simple singularities and simple Lie algebras

currently tenured faculty at U. Belfort.

Here is a summary of his results in English

E. Allaud, PhD spring 03, Nongenericity of variations of Hodge structure for hypersurfaces of high degree,

Now available:

tamuwebmail