Office: Blocker 601H
Office hours: Wed. 1-2pm and Thurs. 10 -11am or by appointment
TAMU math dept homepage
Supported by NSF grants DMS-1405368 and CCF-1814254
Teaching Fall 2018: M689: Quantum computation and information, MW 4:30 - 5:45 Bloc 161.
Honors combined ScB and MS, Mathematics, Brown University, 1986 (MS thesis director, K. Nomizu)
PhD., Mathematics, Duke University, 1990 (director R. Bryant)
Habilitation., Mathematics, Universite Toulouse, 1997 (directeur, C. Simpson)
I organize and co-organize:
Geometry seminar, meeting Mondays 3-4pm Bloc 220 and Fridays 4-5pm Bloc 628.
Working seminar for post-docs and graduate students meeting Mondays, Blocker 628, 5-6pm
Everyone is welcome to the seminars, graduate students
are particularly encouraged to attend.
TAMU seminar calendar
My CV (last updated 10/18)
Brief biographical sketch (updated 11/18)
My travel plans
I am on the editorial board of Foundation of Computational Mathematics, Differential Geometry and its Applications, 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
Geometry 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 to see table of contents and preface, and to order.
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:
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: Kashif Bari, Austin Conner, and Arpan Pal
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
currently post-doctoral fellow at Yongsei Univ. (Seoul)
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,
currently post-doctoral fellow at NC State Univ.
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.
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,
by Suil Kang (Author)
available at Amazon (both paperback and kindle):