Research of Interest

Complexity of Algorithms in Numerical Analysis
Random Real Algebraic Geometry



13. Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems
(with JM. Azais , F. Dalmao, JR. León) (submitted)
12. The polynomial eigenvalue problem is well conditioned for random inputs
(with C. Beltrán ) (submitted SIAM Matrix Analysis)
11. On the asymptotic variance of the number of real roots of random polynomial systems
(with JM. Azais , F. Dalmao, JR. León) (to appear Proceedings of the AMS)
10. A stable, polynomial-time algorithm for the eigenpair problem
(with C. Beltrán , P. Burgisser, F. Cucker, and M. Shub) (accepted for publication JEMS)
9. Condition length and complexity for the solution of polynomial systems
(with C. Beltrán , P. Burgisser, F. Cucker, and M. Shub) Found. Comput. Math. 16 , no. 6, 1401–1422, 2016
8. A Randomized Homotopy for the Hermitian Eigenpair Problem
(with F. Cucker) Foundation of Computational Mathematics 15(1): 281-312, 2015
7. Smale's Fundamental Theorem of Algebra reconsidered
(with M. Shub) Foundation of Computational Mathematics, 14:85–114, 2014
6. Complexity Of Path-Following Methods For The Eigenvalue Problem
Foundation of Computational Mathematics, 14:185-236, 2014
5. A Review Of Some Recent Results On Random Polynomials Over R And Over C
Publicaciones Matemáticas del Uruguay, Proceedings of the IFUM Colloquium, Vol. 12, 1-14, 2011
4. Minimizing The Discrete Logarithmic Energy On The Sphere: The Role Of Random Polynomials
(with C. Beltrán , M. Shub) Trans. Amer. Math. Soc. 363(6), vol 363, 2955-2965, 2011
3. Stochastic-Case Perturbations and Smooth Condition Numbers
J. Complexity 26(2), vol 26, 161-171, 2010
2. On the average number of real roots of a Bernstein polynomial system
(with J.P. Dedieu) J. Complexity 25(4), vol 25, 339-342, 2009
1. Random systems of polynomial equations. The expected number of roots under smooth analysis
(with M. Wschebor) Bernoulli, no.1, 249-266, 2009

PHD Thesis

(Advisors: M. Wschebor, J.P. Dedieu, M. Shub; 2012)

Master Thesis

(Advisors: M. Wschebor, ; 2007)

Degree Thesis

(Advisor: M. Wschebor; 2005)