Here is a summary of all my papers with a brief abstract.

1. Smooth approximations to solutions of nonconvex fully nonlinear elliptic equations.
   Joint work with Luis Caffarelli. Submitted.
2. On the Evans-Krylov theorem.
   Proceedings of the AMS. 138 (2010), 263-265. Joint work with Luis Caffarelli.
3. The Evans-Krylov theorem for non local fully non linear equations.
   Joint work with Luis Caffarelli. Submitted.
4. Regularity results for nonlocal equations by approximation
   Joint work with Luis Caffarelli. Submitted.
5. Eventual regularization for the slightly supercritical quasi-geostrophic equation
   To appear in Annales de l'IHP (C)-ANL.
6. The Dirichlet Problem for the Convex Envelope
   To appear in Transactions of the AMS. Joint work with Adam Oberman.
7. Regularity theory for fully nonlinear integro-differential equations.
   Communications on Pure and Applied Mathematics. 62 (2009) Issue 5, 597--638. Joint work with L. Caffarelli.
8. A characterization of optimal two-phase multifunctional composite designs
   Proc. R. Soc. A 463, Number 2086 (2007). The source code of the numerical tests relevant to this paper can be downloaded here.
9. Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
   Inventiones Mathematicae. 171, Number 2 (2008). Joint work with Luis Caffarelli and Sandro Salsa.
10. Regularity for the nonlinear Signorini problem
    Advances in Mathematics. 217, Issue 3 (2008). Joint work with Manolis Milakis.
11. An extension problem related to the fractional Laplacian
    Communications in Partial Differential Equations, 32 (2007) Issue 8, 1245. Joint work with Luis Caffarelli.
12. Issues in homogenization for problems with nondivergence structure.
    
    Lecture notes of Luis Caffarelli's course in a CIME summer school. Published as a chapter of the book:
    Calculus of variations and nonlinear partial differential equations, 43--74, Lecture Notes in Math., 1927, Springer, Berlin, 2008.
13. Regularity of the obstacle problem for a fractional power of the laplace operator.
    
    Communications on Pure and Applied Mathematics. 60 (2007), no. 1, 67--112.
    This article is based on My PhD Thesis
14. Regularity for fully nonlinear elliptic equations with Neumann boundary data.
    Communications in Partial Differential Equations 31 (2006), No. 8. Joint work with Manolis Milakis.
15. Holder estimates for solutions of integro differential equations like the fractional Laplacian.
    Indiana University Mathematical Journal 55 (2006), 1155-1174.
16. The two membranes problem.
    
    Communications in Partial Differential Equations 30 (2005), no. 1-3, 245--257
17. Weak matrix majorization.
    
    Linear Algebra Appl. 403 (2005), 343--368. Joint work with Francisco Martínez Pería and Pedro Massey