Office: Blocker 601H
Office hours: Tues. 10:30-11:30, Wed. 10-11 or by appointment
TAMU math dept homepage
Fall 2015 teaching: Math 623, Fall 15:
Differential Geometry II
Meeting: MWF 12:40-1:30pm Blocker 202
Fall 2014 I served as Chancellor's Professor at the Simons Institute for the Theory of Computing, UC Berkeley,
I organize and co-organize:My CV (last updated 9/15)
Geometry seminar, meeting Mondays 3-4 Blocker 220 and Fridays 4-5pm Blocker 628.
Working seminar for post-docs and graduate students meeting Wednesdays, Blocker 624,
Everyone is welcome to the seminars, graduate students
are particularly encouraged to attend.
TAMU seminar calendar
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.
PAPERS/PREPRINTS in past 5 years
On the geometry of border rank algorithms for n x 2 by 2 x 2 matrix multiplication (with N. Ryder) Permanent vs determinant: an exponential lower bound assuming
symmetry and a potential path towards Valiant's conjecture (with N. Ressayre)
On minimal free resolutions and the method of shifted partial derivatives in complexity theory (with K. Kefremenko, H. Schenck and J. Weyman) Abelian Tensors (with Mateusz Michalek) Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group (with S. Kumar, Discrete Math. 2015) Complexity of linear circuits and geometry (with F. Gesmundo, G. Hauenstein and C. Ikenmeyer, to appear in FOCM) Geometric Complexity Theory: an introduction for geometers (Ann. U. Ferrara 2015)
Computer aided methods for lower bounds on the border rank (with G. Hauenstein and C. Ikenmeyer, Exper. Math. 2013)
Explicit tensors of border rank at least 2n-2 (J. Pure. Appl. Alg. 2015)
New lower bounds for the rank of matrix multiplication (SICOMP, 2014)
Padded polynomials, their cousins, and geometric complexity theory (with H. Kadish, Communications in Algebra 2014) New lower bounds for the border rank of matrix multiplication (with G. Ottaviani, Theory of Computing 2015) On the third secant variety (with J. Buczynski, JAC 2014) 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, J.London Math. Soc. 2013)
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)
An introduction to Geometric Complexity Theory (to appear in the Newsletter of the EMS) 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.
Current students: Cameron Farnsworth, Fulvio Gesmundo, Younghui Guan, and Curtis Porter.
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
Sungbook: A Collection of Korean Short Stories
available at Amazon (both paperback and kindle):