• 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.)
• 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 special issue 2014)
• Computer aided methods for lower bounds on the border rank (with G. Hauenstein and C. Ikenmeyer)
• Explicit tensors of border rank at least 2n-2
• New lower bounds for the rank of matrix multiplication
• 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, to appear in IMRN)
• 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)
• 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.)
• Survey articles
• 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