Office: Blocker 601H
Office hours: by appointment in summer
TAMU math dept homepage
Supported by NSF grant CCF-1814254
I organize and co-organize:
Geometry seminar, meeting Mondays 3-4pm and Fridays 4-5pm BLOC 302.
Working seminar for post-docs and graduate students meeting Tues. 1-2:30 BLOC 628
RANDOM TENSORS (joint with G. Paouris) Meeting ??
What is representation theory? starting fall 2021 (an expositiory seminar), meeting Thursdays 11-12, BLOC 628
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 are all on arXiv
Recent Papers and those with supplementary files:
Algebraic Geometry and Representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science
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
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 CBMS Regional Conference Series in Mathematics Vol:132Geometry and complexity theory: Cambridge University Press studies in advanced mathematics 169. Click here to see a draft copy
Tensors: Geometry and Applications.
AMS GSM 128. Click here for corrections and additions
Cartan For Beginners: Differential geometry via moving frames and exterior differential systems,
Second Edition (with T. Ivey) AMS GSM 175
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
Current students: Chia-Yu Chang, Runshi Geng, and Arpan Pal
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,