Submitted Papers

• High order numerical methods to approximate the singular value decomposition (with J-C. Yakoubsohn). 2023

Publications

1. Characterization of Logarithmic Fekete Critical Configurations of at Most Six Points in All Dimensions  (with L. Bentancur,  F. Carrasco, M. Fiori, M. Valdes and  M. Velasco).  ISSAC 2025

2. On the logarithmic energy of solutions to the polynomial eigenvalue problem (with F.Carrasco, M. Fiori)
   Constructive Approximation (accepted), 2025

3. On a general Kac-Rice formula for the measure of a level set (with JM. Azais , JR. León).
   Annals of Applied Probability 2025, Vol. 35, No. 3, 1828-1851. (http://dx.doi.org/10.1214/25-AAP2158)

4. Random and mean Lyapunov exponts for Gln(R) (with Gautam Chinta, Siddhartha Sahi, Michael Shub) (DOI: https://doi.org/10.1017/etds.2023.106, 
   Ergodic Theory and Dynamical Systems, 2023).

5. On the finiteness of the moments of the measure of level sets of random fields (with JM. Azais , F. Dalmao, JR. León, E. Mordecki )
   Brazilian Journal of Probability and Statistics, Vol. 37, No. 1, 219–245, 2023

6. 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

7. Central Limit Theorem for the number of real roots of Kostlan Shub Smale random polynomial systems (with JM. Azais , F. Dalmao, JR. León)
   American Journal of Mathematics,  Volume 143, Number 4, pp. 1011-1042, 2021

8. 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

9. 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

10. 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

11. 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

12. Complejidad en análisis numérico y el problema de valores propios
    Publicaciones Matemáticas del Uruguay, Vol. 17, PP 109–118,  S 0797-1443, 2019

13. 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 

14. A Randomized Homotopy for the Hermitian Eigenpair Problem (with F. Cucker)
    Foundation of Computational Mathematics 15(1): 281-312, 2015

15. Smale's Fundamental Theorem of Algebra reconsidered (with M. Shub)
    Foundation of Computational Mathematics, 14:85–114, 2014

16. Complexity Of Path-Following Methods For The Eigenvalue Problem
    Foundation of Computational Mathematics, 14:185-236, 2014 

17. 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

18. 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

19. Stochastic-Case Perturbations and Smooth Condition Numbers
    J. Complexity 26(2), vol 26, 161-171, 2010

20. 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

21. Random systems of polynomial equations. The expected number of roots under smooth analysis (with M. Wschebor)
    Bernoulli, no.1, 249-266, 2009

Thesis

• PHD Thesis:   "Complexity and Random Polynomials" (Advisors: M. Wschebor, J.P. Dedieu, M. Shub; 2012) 

• Master Thesis: "Sistemas Polinomiales Aleatorios" (Advisor: M. Wschebor, ; 2007)

• Degree Thesis: "Matrices Aleatorias y Número de Condición:  (Advisor: M. Wschebor; 2005)

Links to Some Talks