Office: Milner 329
TAMU math dept homepage
Office hours: Mon. 1-2pm, Thurs. 10:30-11:30 and by appointment
Teaching Fall 2013: Math 662, Representation theory, MWF 9:10-10am Block 624
I organize and co-organize:My CV (last updated 1/13)
Working seminar in geometry meeting Tuesdays, Milner 317, 2:15-3:30pm.
Geometry seminar, meeting Fridays 4-5pm Milner 216.
Working seminar for post-docs and graduate students meeting Thursdays, Milner 317,
Everyone is welcome to the seminars, graduate students
are particularly encouraged to attend.
TAMU seminar calendar
My travel plans
I am a co-organizer of the August 19 - 23, 2013 conference
Differential Geometry and its Applications, Brno, Cech Republic, and will
be organizing a special session on geometric complexity theory there.
Co-organizing (with J. Pitts and C. Robles) Texas Geometry and Topology Conference Oct 11-13 2013
Co-organizing (with P. Burgisser, K. Mulmuley and B. Sturmfels) a semeseter long program Fall 2014
Algorithms and Complexity in Algebraic Geometry
to be held at the Simons Institute for Theory of Computing, UC Berkeley.
I am on the editorial board of Differential Geometry and its Applications
and Linear Algebra and its Applications
PAPERS/PREPRINTS in past 5 years
Complexity of linear circuits and geometry (with F. Gesmundo, G. Hauenstein and C. Ikenmeyer) Geometric Complexity Theory: an introduction for geometers Computer aided methods for lower bounds on the border rank (with G. Hauenstein and C. Ikenmeyer, to appear in Exper. Math.)
Explicit tensors of border rank at least 2n-2 New lower bounds for the rank of matrix multiplication (to appear in SICOMP)
Padded polynomials, their cousins, and geometric complexity theory (with H. Kadish, to appear in Communications in Algebra) New lower bounds for the border rank of matrix multiplication (with G. Ottaviani) On the third secant variety (with J. Buczynski, to appear in JAC) On the geometry of Tensor Network States (with Y. Qi and K. Ye, QIC, 2012) Equations for secant varieties of Veronese and other varietites (with G. Ottaviani, Annali di Matematica Pura e Applicata, 2013) Fubini-Griffiths-Harris rigidity of homogeneous varieties (with C. Robles, IMRN 2013) Determinental equations for secant varieties and the Eisenbud-Koh-Stillman conjecture (with J. Buczynski and A. Ginesky, to appear in J. London Math. Soc.)
Hypersurfaces with degenerate duals and the Geometric Complexity Theory Program (with L. Manivel and N. Ressayre, CMH 2013) P versus NP and geometry ( J. Symb. Comp.2010, MEGA 2009 special issue)
Ranks of tensors and a generalization of secant varieties (with J. Buczynski, LAA special issue on tensors 2013) An overview of mathematical issues arising in the Geometric complexity theory approach to VP \neq VNP (with P. Buergisser, L. Manivel and J. Weyman, SIAM J. Comp. 2011) Holographic algorithms without matchgates (with Jason Morton and Serguei Norine, LAA special issue on tensors 2013) On the ranks and border ranks of symmetric tensors (with Z. Teitler, FOCM 2010) Maple file to be read with billards article below (also click here for text version) On the Debarre-deJong and Beheshti-Starr conjectures on varieties with too many lines (with O. Tommasi, Mich. Math. J. 2010) Lines on hypersurfaces (with C. Robles, J. London Math. Soc. 2010) On secant varieties of compact Hermitian symmetric spaces (with J. Weyman, J. Pure Appl. Alg. 2009) Fubini's theorem in codimension two (with C. Robles, Crelle 2009) Fubini-Griffiths-Harris rigidity and Lie algebra cohomology (with C. Robles, (Asian Math. J. 2013)
all articles (since 2006)
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
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 (with T. Ivey)AMS GSM 61 . To see the table of contents, preface, and selected pages click here
To order the book from the AMS, click here.
to see corrections to text, click here
math reviews of all published papersLuke Oeding, PhD May 2009, Defining equations of the varietyof principal minors solved a conjecture of Holtz and Sturmfels.
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
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
Ming Yang, PhD Sept. 2012, On partial and generic uniqueness of block term tensor decompositions in signal processing, solving questions originating in signal processing.
Frederic Holweck, PhD fall 04, Dual varieties, simple singularities and simple Lie algebras
Here is a summary of his results in English
E. Allaud, PhD spring 03, thesis: Nongenericity of variations of Hodge structure for hypersurfaces of high degree,
published in Duke. Math. J.
New to the area? Here are some Brazos Valley links
Supported by NSF grant 1006353