## Papers

- Computer-assisted proofs in PDE: a survey.

Submitted (2018).

- On the existence of stationary patches.

Submitted (2018).

- Spectral determination of semi-regular polygons, with A. Enciso.

Submitted (2017).

- Global solutions for the generalized SQG patch equation, with D. Córdoba and A. Ionescu.

Submitted (2017).

- Uniformly rotating smooth solutions for the incompressible 2D Euler equations, with A. Castro and D. Córdoba.

Arch. Ration. Mech. Anal., to appear (2018).

- Global smooth solutions for the inviscid SQG equation, with A. Castro and D. Córdoba.

Memoirs of the AMS, to appear (2017).

- A note on stability shifting for the Muskat problem II: Stable to Unstable and back to Stable, with D. Córdoba and A. Zlatoš.

Analysis & PDE, 10, no. 2, 367-378 (2017).

- Uniformly rotating analytic global patch solutions for active scalars, with A. Castro and D. Córdoba.

Annals of PDE, 2, no. 1, 1-34 (2016).

- Splash singularities for the free boundary Navier-Stokes equations, with A. Castro, D. Córdoba, C. Fefferman and F. Gancedo.

Submitted (2015).

- A note on stability shifting for the Muskat problem, with D. Córdoba and A. Zlatoš.

Phil. Trans. R. Soc. A, 373, no. 2050, 20140278 (2015).

- Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations, with A. Castro and D. Córdoba.

Duke Mathematical Journal, 165, no. 5, 935-984 (2016).

- Structural stability for the splash singularities of the water waves problem, with A. Castro, D. Córdoba, C. Fefferman and F. Gancedo.

Discrete and Continuous Dynamical Systems - A, 34, no. 12, 4997-5043 (2014).

- Remarks on geometric properties of SQG sharp fronts and $\alpha$ patches, with A. Castro, D. Córdoba and A. M. Zamora.

Discrete and Continuous Dynamical Systems - A, 34, no. 12, 5045-5059 (2014).

- On turning waves for the inhomogeneous Muskat problem: a computer-assisted proof, with R. Granero-Belinchón.

Nonlinearity, 27, no. 6, 1471-1498 (2014).

- Finite time singularities for water waves with surface tension, with A. Castro, D. Córdoba, C. Fefferman and F. Gancedo.

J. Math. Phys., 53, no. 11, 115622 (2012). Special Issue "Incompressible Fluids, Turbulence and Mixing".

- Finite time singularities for the free boundary incompressible Euler equations, with A. Castro, D. Córdoba, C. Fefferman and F. Gancedo.

Annals of Math, 178, no. 3, 1061-1134 (2013).

- Splash singularity for water waves, with A. Castro, D. Córdoba, C. Fefferman and F. Gancedo.

Proc. Natl. Acad. Sci., 109, no. 3, 733-738 (2012).

- The Bounded Confidence Model Of Opinion Dynamics, with C. Graham and J.-Y. Le Boudec.

Math. Mod. Meth. Appl. Sci. 22, num. 2, 1150007(1-46), (2012).

- Comment on "Mixing beliefs among interacting agents",
with J.-Y. Le Boudec.

Adv. Complex Syst., 15, no. 7, 1250028(1-7), (2012).