fractal
  

Research of Interest

Complexity of Algorithms in Numerical Analysis
Random Real Algebraic Geometry

 

Preprints

17. Random and mean Lyapunov exponts for $Gln(R)$
(with Gautam Chinta, Siddhartha Sahi, Michael Shub) (arXiv:2206.01091)
16. On the finiteness of the moments of the measure of level sets of random fields
(with JM. Azais , F. Dalmao, JR. León, E. Mordecki ) (arXiv:1909.10243)
 

Publications

15. Central Limit Theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems
(with JM. Azais , F. Dalmao, JR. León) Journal of Complexity - Volume 72, 2022(arXiv:1808.02967)
14. Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems
(with JM. Azais , F. Dalmao, JR. León) To appear in American Journal of Mathematics 2019
13. Conditions for the finiteness of the moments of the volume of level sets.
(with JM. Azais , D. Ginsbourger, JR. León) Electron. Commun. Probab. Volume 24, paper no. 17, 8 pp., 2019
12. The polynomial eigenvalue problem is well conditioned for random inputs
(with C. Beltrán ) SIAM J. Matrix Anal. Appl., 40(1), 175–193. (19 pages) 2019
11. On the asymptotic variance of the number of real roots of random polynomial systems
(with JM. Azais , F. Dalmao, JR. León) Proc. Amer. Math. Soc. 146, 5437-5449, 2018
10. A stable, polynomial-time algorithm for the eigenpair problem
(with C. Beltrán , P. Burgisser, F. Cucker, and M. Shub) Journal of the European Mathematical Society, Volume 20, Issue 6, pp. 1375–1437, 2018
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)