Research Publications:

13. Desde Fermat, Lamé y Kummer hasta Iwasawa: Una introducción a la teoría de Iwasawa, to appear in La Gaceta de la Real Sociedad Matemática Española (J. of the Royal Mathematical Society of Spain) (accepted).

12. Bernoulli-Hurwitz numbers, Wieferich primes and Galois representations, Journal of Number Theory 130 (2010), pp. 539-558.

11. Bounds for the torsion of elliptic curves over extensions with bounded ramification (joint with Benjamin Lundell), International Journal of Number Theory, Volume: 6, Issue: 6 (2010), pp. 1293-1309.

10. Elliptic curves of maximal rank, (joint work with Julian Aguirre and Juan Carlos Peral), in Revista Matematica Iberoamericana, proceedings of the conference "Segundas Jornadas de Teoria de Numeros". (2010), pp. 1293-1309.

9. On the product of twists of rank two and a conjecture of Larsen, Ramanujan Journal,Vol 19, n 1, May 2009, pp. 53-61.

8. On products of quadratic twists and ranks of elliptic curves over large fields (joint with Bo-Hae Im), Journal of the London Mathematical Society, Vol 79, part 1, Feb. 2009, pp. 1-14.

7. Ranks of abelian varieties over infinite extensions of the rationals, Manuscripta Mathematica, Volume 126, Number 3,  July 2008, pp. 393-407.

6. Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer's criterion, in RACSAM (Journal of the Royal Academy of Science of Spain),
Vol 101 (1), 2007.

5. Constructing elliptic curves over Q(t) with moderate rank, (joint with Scott Arms and Steven J.Miller), Journal of Number Theory, Volume 123, Issue 2, April 2007, pp. 388-402.

4. On elliptic units and p-adic Galois representations attached to elliptic curves, Journal of Number Theory, Vol. 117, Issue 2, (2006), pp. 439-470.

3. On the surjectivity of Galois representations attached to elliptic curves over number fields, Acta Arithmetica, Vol. 117, No. 3, (2005), pp. 283-291.

2. On certain closed subgroups of SL(2,Z_p[[X]]), Revista Colombiana de Matemáticas, Vol 39 (2005), pp. 13-19.

1. Buscando puntos racionales en curvas elípticas: Métodos explícitos, La Gaceta de la Real Sociedad Matematica Española (J. of the Royal Mathematical Society of Spain), Vol. 8 (2005), n 2, 471-488.