Survey articles On tangential varieties of rational homogeneous varieties (with J. Weyman, Jour. LMS 2007) Computer aided methods for lower bounds on the border rank (with G. Hauenstein and C. Ikenmeyer)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)

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 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