Mauricio Velasco

Articles and Preprints:

Characterization of Logarithmic Fekete Critical Configurations of at Most Six Points in All Dimensions (with D. Armentano, L. Bentancour, F. Carrasco, M. Fiori, and M. Valdez) [ArXiv] Submitted.
Nonnegativity certificates on real algebraic surfaces (with G. Blekherman, G.G. Smith, and R. Sinn) [ArXiv] Submitted.
Spurious local minima in nonconvex sum-of-squares optimization (with G. Blekherman, R. Sinn, and S. Zhang) [ArXiv] Submitted.
Graph neural networks and non-commuting operators (with S. Villar, K. O'Hare, and B. Rychtenberg) Proceedings of NeurIPS 2024.
Universal transferability for GNNs via graphons (with S. Villar, K. O'Hare, and B. Rychtenberg) Proceedings of ASILOMAR 2024.
Harmonic hierarchies for polynomial optimization (with S. Cristancho)[ArXiv] SIAM Journal on Optimization vol. 34, pp. 590–615, (2024).
Moment-SOS hierarchy and exit location of stochastic processes (with M. Junca and D. Henrion) [Journal] Numerical Algebra, Control and Optimization (2024).
Smart Pooling: AI-powered COVID-19 testing (with J. Madrid-Wolff, P. Arbelaez, M. Forero-Shelton, J.M. Pedraza, et al.) [MedrXiv] Nature Scientific Reports, Vol. 12 (2022).
Constructing Partial MDS Codes from Reducible Curves (with T. Bogart, A. Horlemann-Trautmann, D. Karpuk and A. Neri) [ArXiv] SIAM Journal on Discrete Mathematics, Vol. 35, Issue 4, pp. 2946-2970, (2021).
Sums of Squares: A Real Projective Story (with G.Blekherman, R.Sinn and G.G.Smith) [ArXiv] Notices of the AMS, Vol. 68, Issue 5, pp. 734-747, (2021).
Sums of Squares and Quadratic Persistence on Real Projective Varieties (with G.Blekherman, R.Sinn and G.G.Smith) [ArXiv ] Journal of the European Mathematical Society Vol. 24, Issue 3, pp. 925-965, (2021).
Approximate super-resolution of positive measures in all dimensions (with C. Hernandez, H. Garcia and M. Junca) [ArXiv] Applied and Computational Harmonic Analysis, Vol. 52, pp. 251–278 (2020).
Algebraic Geometry and sums of squares (book chapter) Proceedings of Symposia in Applied Mathematics (PSAPM), part of the volume entitled *Sums of Squares: Theory and Applications* edited by P. Parrilo and R. Thomas. (2020).
Local angles and dimension estimation from data on manifolds (with M. Diaz and A.J. Quiroz) [ArXiv] Journal of Multivariate Analysis, 173, pp. 229–247 (2019).
Sharp Degree Bounds for Sum-of-Squares Certificates on Projective Curves (with G. Blekherman and G.G. Smith) [ArXiv] Journal des Mathématiques Pures et Appliquées (JMPA) (2019)
Do Sums of Squares Dream of Free Resolutions? (with G. Blekherman and R. Sinn) [ArXiv] SIAM Journal on Applied Algebra and Geometry (2017)
Compressed sensing of data with a known distribution (with M. Diaz, M. Junca and F. Rincón) [ArXiv] Applied and Computational Harmonic Analysis (2017)
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.
Semidefinite approximations of conical hulls of measured sets (with J. Romero) [ArXiv] Discrete and Computational Geometry (2014)
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.
Frames and Degenerations of Monomial Ideals (with I. Peeva) [pdf] Trans. Amer. Math. Soc., 363 (2011), no. 4, 2029–2046.
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.