Office: Milner 329
E-mail: jml@math.tamu.edu
TAMU math dept homepage
Office hours: Mon. 1:15-2:15pm, Thurs. 10:30-11:30 and by appointment
I organize and co-organize:My CV (last updated 1/12)
Working seminar in geometry meeting Tuesdays, Milner 317, 2:15-3:30pm.
Geometry seminar, meeting Fridays 4-5pm Milner 216.
Joint geometry-string theory seminar, meeting monthly Fridays 4-5pm Milner 216
Working seminar for post-docs and graduate students meeting Thursdays, Milner 317,
2:15-3:30pm
Everyone is welcome to the seminars, graduate students
are particularly encouraged to attend.
TAMU seminar calendar
My travel plans
I am co-organizing (with J. Harris) here at TAMU, April 25-27 2012, a workshop: Questions in geometry arising in the sciences. This will be in conjunction with Joe Harris' Maxson lectures and with the annual TAGS (Texas Algebraic Geometry Symposium) to be held here at A&M April 27-29 2012. The workshop is partially supported by IMA.
I am co-organizing (with S. Kumar and J. Weyman) an AMS MRC: Geometry and Representation Theory Related to Geometric Complexity and Other Variants of P v. NP. June 17-23, 2012, Snowbird, Utah
July 1-14, I am giving a summer course at Cortona with M. Mella: Tensors: Waring problems and Geometric Complexity Theory
Now available: Tensors: Geometry and Applications.
AMS GSM 128. Click here to see table of contents and preface, and to order.
I am on the editorial board of Differential Geometry and its Applications
Survey articlesRECENT PAPERS/PREPRINTS
Padded polynomials, their cousins, and geomtric complexity theory (with H. Kadish) New lower bounds for the border rank of matrix multiplication (with G. Ottaviani) On the third secant variety (with J. Buczynski) 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, 2011) Fubini-Griffiths-Harris rigidity of homogeneous varieties (with C. Robles, IMRN, 2012) Determinental equations for secant varieties and the Eisenbud-Koh-Stillman conjecture (with J. Buczynski and A. Ginesky)
Hypersurfaces with degenerate duals and the Geometric Complexity Theory Program (with L. Manivel and N. Ressayre, to appear in CMH) 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, to appear in LAA special issue on tensors) 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 2012) 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, to appear in Asian Math. J.)
Geometry and the complexity of matrix multiplication (survey article, Bull. AMS 2008) Generalizations of Strassen's equations for secant varieties of Segre varieties (with L. Manivel, Comm. Algebra 2008)
On tangential varieties of rational homogeneous varieties (with J. Weyman, Jour. LMS 2007) On the ideals and singularities of secant varieties of Segre varieties (with J. Weyman, Bull. LMS 2007) Legendrian varieties (with L. Manivel, Asian J. Math 2007)
The border rank of the multiplication of two by two matrices is seven (JAMS 19(2006) p447-459)
The sextonions and E_{7 1/2} (with L. Manivel) (Advances in Math 201(2006) p143-179)
A universal dimension formula for complex simple Lie algebras (with L.Manivel) (Advances in Math 201(2006) p379-407)
Griffiths-Harris rigidity of compact Hermitian symmetric spaces (JDG 74(2006) p 395-405.)
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
math reviews of all published papersMy student Luke Oeding finished his PhD May 2009, his paper on Defining equations of the variety
of principal minors solved a conjecture of Holtz and Sturmfels.
My student Frederic Holweck defended his thesis in fall 04 on dual varieties, simple singularities and simple Lie algebras
Here is a summary of his results in English
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