Submitted Papers

• On the logarithmic energy of solutions to the polynomial eigenvalue problem (with F.Carrasco, M. Fiori) 2024

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

• On a general Kac-Rice formula for the measure of a level set (with JM. Azais , JR. León). 2023

Publications

1. 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).

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

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

10. 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 

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

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

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

14. 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

15. 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

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

17. 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

18. 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