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