Do Sums of Squares Dream of Free Resolutions? (with G. Blekherman and R. Sinn) [ArXiv ] Submitted
Sharp Degree Bounds for Sum-of-Squares Certificates on Projective Curves (with G. Blekherman and G.G. Smith) [ArXiv ] Submitted
Compressed sensing of data with a known distribution (with M. Diaz, M. Junca and F. Rincón) [ArXiv ] Submitted
Semidefinite approximations of conical hulls of measured sets (with J.Romero) [ArXiv ] Submitted
Test sets for nonnegativity of polynomials invariant under a finite reflection group (with J.G. Acevedo) [ArXiv ] J. Pure Appl. Algebra, 220 (2016)
Sums of squares and varieties of minimal degree (with G. Blekherman and G.G. Smith) [ArXiv ] Journal of the American Mathematical Society (JAMS), 29 (2016)
A lower bound for the determinantal complexity of a hypersurface (with J. Alper and T.C. Bogart) [ArXiv ] Foundations of Computational Mathematics (FOCM), (2015).
Gap vectors of real projective varieties (with G. Blekherman, S. Iliman and M. Kubitzke) [ArXiv ] Advances in Mathematics (2015), pp. 458-472.
Dual toric codes and polytopes of degree one (with V. Gauthier) [ArXiv ] SIAM J. Discrete Math., 29(1) (2015), 683-692.
Linearization functors on real convex sets. [ArXiv ] SIAM Journal on Optimization, 25 (1) (2015), 1-27.
The maximum cut problem for blow-ups of multiprojective space (with M. Junca) [ArXiv ] J. Algebraic Combin., 38 (2013), no. 4, 797-827.
Big rational surfaces (with D. Testa and A. Varilly-Alvarado) [ArXiv] Math. Ann., 351 (2011), no. 1,95-107.
Blow-ups of P^{n-3} at n points and Spinor varieties (with B. Sturmfels). [ArXiv ] J. Commut. Algebra , 2 (2010), no. 2,223-244.
A syzygetic approach to the smoothability of zero-dimensional schemes (with D. Erman). [ArXiv ] Advances in Mathematics, 224 (2010), no. 3,1143-1166.
Cox rings of degree one Del Pezzo surfaces (with D. Testa and A. Varilly-Alvarado). [ArXiv ] Algebra Number Theory, 3 (2009), no. 7,763-795.
Hilbert Schemes of eight points (with D. Cartwright, D. Erman and B. Viray).[ArXiv ] Algebra and Number Theory, 3 (2009), no. 7,729-761.
Picard graded Betti numbers and the defining ideals of Cox rings (with A.Laface). [ArXiv ]. Journal of Algebra, 322 (2009), no. 2, 353-372.
A survey on Cox rings (with A.Laface). [.pdf ] Geometriae Dedicata ,139 (2009), 269-287.
Minimal free resolutions that are not supported by a CW-complex. [pdf ] Journal of Algebra, 319 (2008), no. 1, 102-114.
Grobner bases, monomial group actions and the Cox rings of Del Pezzo surfaces (with M. Stillman and D. Testa). [pdf ] Journal of Algebra, 316 (2007), no. 2, 777-801.