Matemática pura

28. (con P. Candela) On the dimension of additive sets, Acta Arith. 167 (2015), no. 1, 91-100.
27. Random generators of the symmetric group: diameter, mixing time and spectral gap (con Á. Seress y A. Zuk), J. of Algebra. 421 (2015), 349-368.
26. The ternary Goldbach conjecture is true, prepublicación.
25. Major arcs for Goldbach's problem, prepublicación.
24. (con D. Platt) Numerical verification of the ternary Goldbach conjecture up to 8.875e30, Experiment. Math. 22 (2013), no. 4, 406-409
23. Growth in groups: ideas and perspectives, Bull. Am. Math. Soc. 52 (2015), no. 3, 357-413.
22. (con N. Gill y M. Rudnev) On growth in an abstract plane, Proc. Am. Math. Soc. 143 (2015), no. 8, 3593-3602
21. Minor arcs for Goldbach's problem, prepublicación.
20. Bounds on the diameter of Cayley graphs of the symmetric group (con J. Bamberg, N. Gill, T. Hayes, Á. Seress y P. Spiga), J. Algebraic Combin. 40 (2014), no. 1, 1-22.
19. Square-free values of f(p), f cubic, Acta Math. 213 (2014), no. 1, 107-135.
Th3. Groupes, courbes et croissance, tesis de habilitación, Paris-Sud (Orsay).
18. On the diameter of permutation groups (con Á. Seress), Annals of Math. 179 (2014), no. 2, . 1, 107-135. 611-658.
17. Deterministic methods to find primes (como D. H. J. Polymath, con T. Tao y E. Croot), Math. Comp. 81 (2012), no. 278, 1233-1246.
16. Growth in solvable subgroups of GLr(Z/pZ) (con N. Gill), Math. Annalen 360 (2014), no. 1-2, 157-208.
15. Growth of small generating sets in SLn(Z/pZ) (con N. Gill), Int. Math. Res. Notices., Vol. 2011, 4226--4251 .
14. An explicit incidence theorem in Fp (con M. Rudnev), Mathematika, 57 (2011), no. 1, 135--145.
13. Improving Roth's theorem in the primes (con A. de Roton), Int. Math. Res. Notices. (2011), Vol. 2011, 767--783.
12. Growth in SL3(Z/pZ), J. Eur. Math. Soc. (JEMS), vol. 13, no. 3, pp. 761--851.
11. Power-free values, repulsion between points, differing beliefs and the existence of error, CRM Proceedings and Lecture Notes, v. 46 (2008), 81-88.
10. How small must ill-distributed sets be? (con A. Venkatesh), in: Chen, W. W. L. (ed.) et al., Analytic number theory. Essays in honour of Klaus Roth on the occasion of his 80th birthday. Cambridge University Press, 2009, pp. 224-234.
9. Growth and generation in SL2(Z/pZ), Ann. of Math. 167 (2008), 601-623.
8. The parity problem for irreducible polynomials, prepublicación.
7. Power-free values, large deviations and integer points on irrational curves, J. Théor. Nombres Bordeaux 19 (2007), 433-472.
6. The parity problem for reducible polynomials, J. London Math. Soc. (2) 73 (2006), 415-435.
5. Integral points on elliptic curves and 3-torsion in class groups (con A. Venkatesh), J. Amer. Math. Soc. 19 (2006), 527--550.
4. Root numbers and ranks over global function fields (con B. Conrad and K. Conrad), Adv. Math. 198 (2005), 684--731.
3. On the behaviour of root numbers in families of elliptic curves, prepublicación.
2. On the square-free sieve, Acta Arith. 115 (2004), 349-402.
Th2. Root numbers and the parity problem, tesis de doctorado, Princeton University, abril 2003, math.NT/0305435.
1. Enumeration of tilings of diamonds and hexagons with defects (con I. M. Gessel), Electron. J. Combin. 6 (1999), no. 1, R16.
Th1. Edge effects on local statistics in lattice dimers: a study of the Aztec diamond (finite case), tesis de bachillerato, Brandeis University, May 1998, math.CO/0007136.

Monografías - Matemática pura

M2. The ternary Goldbach problem, por aparecer en Ann. of Math. Studies.
M1. Azar y aritmética, Monografías del Instituto de Matemática y Ciencias Afines, v. 50, IMCA, Lima, Perú.
Nota: la monografía M2 reemplaza a las prepublicaciones 26, 25 y 21.

Artículos para el gran público - Matemática pura

GP3. The ternary Goldbach problem, por aparecer en Proc. ICM (Korea, 2014).
GP2. La conjecture de Goldbach ternaire, por aparecer en Gaz. Math.
GP1. La conjetura débil de Goldbach, Gac. R. Soc. Mat. Esp. 16 (2013), no. 4.
Nota: GP1, GP2 y (en parte) GP3 están basados en mi texto en inglés sobre el asunto.

Historia y pedagogía

HP3. A modern vision of the work of Cardano and Ferrari on quartics (with M. Helfgott), CONVERGENCE, an online journal of the Mathematical Association of America, julio 2009.
HP2. A noncalculus proof that Fermat's principle of least time implies the law of refraction (with M. Helfgott), Am. J. Phys. 70 (2002), no. 12, 1224-1225.
HP1. Maxima and minima before Calculus (con M. Helfgott), Pro Mathematica XII (1998), nos. 23-24, 135-158.

Compresión de datos y teoría de la información

Ya no estoy activo en estos campos. Ver Martin Cohn y James Storer.