Hölder continuous dissipative solutions of ideal MHD with nonzero helicity, preprint (with J. Peñafiel-Tomás and D. Peralta-Salas).
Desingularization of vortex sheets for the 2D Euler equations, preprint (with A.J. Fernández and D. Meyer).
Steady 3D Euler flows via a topology-preserving convex integration scheme, preprint (with J. Peñafiel-Tomás and D. Peralta-Salas).
Local limits of high-energy eigenfunctions on integrable billiards, preprint (with A. García-Ruiz and D. Peralta-Salas).
A Calderón problem for Beltrami fields, preprint (with C. Valero).
Positive solutions to general overdetermined boundary problems, preprint (with P. Hidalgo-Palencia and X. Ros-Oton).
Solutions to general elliptic equations on nearly geodesically convex domains with many critical points, preprint (with F. Gladiali and M. Grossi).
Smooth nonradial stationary Euler flows on the plane with compact support, preprint (with A.J. Fernández and D. Ruiz).
Convexity of Whitham's highest wave, preliminary version (with J. Gómez-Serrano and B. Vergara).
Finite time singularity formation for angle-crested water waves, preprint (with D. Córdoba and N. Grubic).
An extension theorem for weak solutions of the 3D incompressible Euler equations and applications to singular flows, Forum Math. Pi, in press (with J. Peñafiel-Tomás and D. Peralta-Salas).
Nonexistence of Courant-type nodal domain bounds for eigenfunctions of the Dirichlet-to-Neumann operator, J. Eur. Math. Soc., in press (with A. Pistoia and L. Provenzano).
Schiffer-type problems and nonradial stationary Euler flows with compact support, Journées EDP (2024), in press.
A Schiffer-type problem for annuli with applications to stationary planar Euler flows, Duke Math. J., in press (with A.J. Fernández, D. Ruiz, and P. Sicbaldi).
Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimates, Anal. PDE, in press (with A. Shao and B. Vergara).
Optimal convex domains for the first curl eigenvalue, Trans. Amer. Math. Soc., in press (with W. Gerner and D. Peralta-Salas).
Optimal metrics for the first curl eigenvalue on 3-manifolds, Calc. Var. PDE, in press (with W. Gerner and D. Peralta-Salas).
Isolated steady solutions of the 3D Euler equations, Proc. Natl. Acad. Sci. 122 (2025) 12 (with W. Kepplinger and D. Peralta-Salas).
MHD equilibria with nonconstant pressure in nondegenerate toroidal domains, J. Eur. Math. Soc. 27 (2025) 2251–2291 (with A. Luque and D. Peralta-Salas).
Obstructions to topological relaxation for generic magnetic fields, Arch. Ration. Mech. Anal. (2025) 249:6 (with D. Peralta-Salas).
Entanglement of vortices in the Ginzburg-Landau equations for superconductors, Comm. Math. Phys. (2024) 405:155 (with D. Peralta-Salas).
Small spheres of prescribed mean curvature in Riemannian manifolds, J. Funct. Anal. 286 (2024) 110415 (with A.J. Fernández and D. Peralta-Salas).
Inverse localization and global approximation for some Schrödinger operators on hyperbolic spaces, J. Math. Phys. 65, 062102 (2024) (Editor's Pick) (with A. García-Ruiz and D. Peralta-Salas).
Critical point asymptotics for Gaussian random waves with densities of any Sobolev regularity, Adv. Math. 437 (2024) 109450 (with D. Peralta-Salas and A. Romaniega).
Non-integrability and chaos for natural Hamiltonian systems with a random potential, Adv. Math. 437 (2024) 109448 (with D. Peralta-Salas and A. Romaniega).
Beltrami fields exhibit knots and chaos almost surely, Forum Math. Sigma 11:e56 (2023) (with D. Peralta-Salas and A. Romaniega).
Local wellposedness for the free boundary incompressible Euler equations with interfaces that exhibit cusps and corners of nonconstant angle, Adv. Math. 433 (2023) 109299 (with D. Córdoba and N. Grubic).
Localization properties of high energy eigenfunctions on flat tori, Int. Math. Res. Not. (2023) 20988-21014 (with A. García-Ruiz and D. Peralta-Salas).
Overdetermined boundary problems with non constant Dirichlet and Neumann data, Anal. PDE 16 (2023) 1989-2003 (with M. Domínguez-Vázquez and D. Peralta-Salas).
Quasi-periodic solutions to the incompressible Euler equations in dimensions two and higher, J. Differential Equations 354 (2023) 170-182 (with D. Peralta-Salas and F. Torres de Lizaur).
Beltrami fields and knotted vortex structures in incompressible fluid flows, Bull. London Math. Soc. 55 (2023) 1059-1103 (with D. Peralta-Salas).
Non-existence of axisymmetric optimal domains with smooth boundary for the first curl eigenvalue, Ann. Sc. Norm. Sup. Pisa 24 (2023) 311-327 (with D. Peralta-Salas).
Limiting measures and energy growth for sequences of solutions to Taubes's Seiberg-Witten equations, J. Geom. Anal. 33 (2023) 269 (with D. Peralta-Salas and F. Torres de Lizaur).
Spectral determination of semi-regular polygons, J. Differential Geom. 122 (2022) 399-419 (with J. Gómez-Serrano).
Asymptotics for the nodal components of non-identically distributed random monochromatic waves, Int. Math. Res. Not. (2022) 774-800 (with D. Peralta-Salas and Á. Romaniega).
Vortex reconnections in classical and quantum fluids, SEMA J. 79 (2022) 127-137 (with D. Peralta-Salas).
Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials, J. Eur. Math. Soc. 23 (2021) 3459-3495 (with A. Shao and B. Vergara).
Self-intersecting interfaces for stationary solutions of the two-fluid Euler equations, Ann. of PDE 7 (2021) 12 (with D. Córdoba and N. Grubic).
Approximation theorems for the Schrödinger equation and quantum vortex reconnection, Comm. Math. Phys. 387 (2021) 1111-1149 (with D. Peralta-Salas).
Piecewise smooth stationary Euler flows with compact support via overdetermined boundary problems, Arch. Ration. Mech. Anal. 239 (2021) 1327-1347 (with M. Domínguez-Vázquez and D. Peralta-Salas).
Ramified local embeddings of singular Riemannian metrics, J. Differential Equations 277 (2021) 38–56 (with N. Kamran).
Beltrami fields with hyperbolic periodic orbits enclosed by knotted invariant tori, Adv. Math. 373 (2020) 107328(46) (with A. Luque and D. Peralta-Salas).
Approximation theorems for parabolic equations and movement of hot spots, Duke Math. J. 168 (2019) 897-939 (with M.A. García-Ferrero and D. Peralta-Salas).
Lorentzian Einstein metrics with prescribed conformal infinity, J. Differential Geom. 112 (2019) 505-554 (with N. Kamran).
Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities, Adv. Math. 351 (2019) 718-760 (with M. Domínguez-Vázquez and D. Peralta-Salas).
A problem of Ulam about magnetic fields generated by knotted wires, Ergodic Th. Dynam. Syst. 39 (2019) 2048-2070 (with D. Peralta-Salas).
Stationary phase methods and the splitting of separatrices, Comm. Math. Phys. 368 (2019) 1297-1322 (with A. Luque and D. Peralta-Salas).
A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator, J. Eur. Math. Soc. 20 (2018) 301-314 (with D. Hartley and D. Peralta-Salas).
The Biot-Savart operator of a bounded domain, J. Math. Pures Appl. 119 (2018) 85-113 (with M.A. García-Ferrero and D. Peralta-Salas).
Stability results, almost global generalized Beltrami fields and applications to vortex structures in the Euler equations, Comm. Math. Phys. 360 (2018) 197-269 (with D. Poyato and J. Soler).
Dislocations of arbitrary topology in Coulomb eigenfunctions, Rev. Mat. Iberoam. 34 (2018) 1361-1371 (with D. Hartley and D. Peralta-Salas).
Existence of knotted vortex structures in stationary solutions of the Euler equations, Proceedings 7ECM (Plenary Talks), EMS, Zurich, 2018 (with D. Peralta-Salas).
Minimal surfaces with micro-oscillations, J. Differential Equations 265 (2018) 3339-3344 (with M.A. García-Ferrero and D. Peralta-Salas).
Knotted structures in high-energy Beltrami fields on the torus and the sphere, Ann. Sci. Éc. Norm. Sup. 50 (2017) 995-1016 (with D. Peralta-Salas and F. Torres de Lizaur).
Vortex reconnection in the three dimensional Navier-Stokes equations, Adv. Math. 309 (2017) 452-486 (with R. Lucà and D. Peralta-Salas).
Fractional powers of the wave operator via Dirichlet–Neumann maps in anti-de Sitter space, J. Funct. Anal. 273 (2017) 2144-2166 (with M.d.M. González and B. Vergara).
Uniqueness and characterization theorems for generalized entropies, J. Stat. Mech. (2017) 123101 (with P. Tempesta).
On the existence of stationary splash singularities for the Euler equations, Adv. Math. 288 (2016) 922–941 (with D. Córdoba and N. Grubic).
Beltrami fields with a nonconstant proportionality factor are rare, Arch. Ration. Mech. Anal. 220 (2016) 243–260 (with D. Peralta-Salas).
Prescribing the nodal set of the first eigenfunction in each conformal class, Int. Math. Res. Not. 2016, 1-28 (with S. Steinerberger).
Helicity is the only integral invariant of volume-preserving transformations, Proc. Nat. Acad. Sci. 113 (2016) 2035–2040 (with D. Peralta-Salas and F. Torres de Lizaur).
Laplace operator with eigenfunctions whose nodal set is a knot, J. Funct. Anal. 271 (2016) 182–200 (with D. Hartley and D. Peralta-Salas).
Bounded solutions to the Allen-Cahn equation with level sets of any compact topology, Anal. PDE 9 (2016) 1433–1446 (with D. Peralta-Salas).
Topological monsters in elliptic equations and spectral theory, EMS Surv. Math. Sci. 3 (2016) 107–130 (with D. Peralta-Salas).
Existence of knotted vortex tubes in steady fluid flows, Acta Math. 214 (2015) 61–134 (with D. Peralta-Salas).
A singular initial-boundary value problem for nonlinear wave equations and holography in asymptotically anti-de Sitter spaces, J. Math. Pures Appl. 103 (2015) 1053–1091 (with N. Kamran).
Eigenfunctions with prescribed nodal sets, J. Differential Geom. 101 (2015) 197–211 (with D. Peralta-Salas).
Determining an asymptotically AdS spacetime from data on its conformal boundary, Gen. Relativity Gravitation 47 (2015) 147 (with N. Kamran).
Critical points and geometric properties of Greens functions on open surfaces, Ann. Mat. Pura Appl. 194 (2015) 881–901 (with D. Peralta-Salas).
Knotted vortex lines and vortex tubes in stationary Euler flows, Newsletter EMS 96 (2015) 26–33 (with D. Peralta-Salas).
An exactly solvable deformation of the Coulomb problem associated with the Taub–NUT metric, Ann. Phys. 351 (2014) 540–557 (with A. Ballesteros, F.J. Herranz, O. Ragnisco, and D. Riglioni).
Geometric problems in PDEs with applications to mathematical physics, SEMA J. 65 (2014) 1–11.
Submanifolds that are level sets of a solution to an elliptic PDE, Adv. Math. 249 (2013) 204–249 (with D. Peralta-Salas).
Some geometric conjectures in harmonic function theory, Ann. Mat. Pura Appl. 192 (2013) 49–59 (with D. Peralta-Salas).
Thin vortex tubes in the stationary Euler equation, Journées EDP (2013) IV (with D. Peralta-Salas).
Knots and links in steady solutions of the Euler equation, Ann. of Math. 175 (2012) 345–367 (with D. Peralta-Salas).
On the spectrum of Y^{p,q} manifolds, J. High Energy Phys. 1205 (2012) 009(37) (with F. Chen, K. Dasgupta, N. Kamran, and J. Seo).
Causality and the conformal boundary of AdS in real-time holography, Phys. Rev. D 85 (2012) 106016(5) (with N. Kamran).
Critical points of Green’s functions on complete manifolds, J. Differential Geom. 92 (2012) 1–29 (with D. Peralta-Salas).
Thermodynamics of spin chains of Haldane–Shastry type and one-dimensional vertex models, Ann. Phys. 327 (2012) 2627–2665 (with F. Finkel and A. González-López).
Nondegeneracy of the eigenvalues of the Hodge Laplacian on 3-manifolds for generic metrics, Trans. Amer. Math. Soc. 364 (2012) 4207–4224 (with D. Peralta-Salas).
Coulomb systems on Riemannian manifolds and stability of matter, Ann. Henri Poincaré 12 (2011) 723–741.
Spinor Green’s functions via spherical means on products of space forms, J. Geom. Phys. 61 (2011) 180–190 (with N. Kamran).
On two superintegrable nonlinear oscillators in N dimensions, Int. J. Theor. Phys. 50 (2011) 2268–2277 (with A. Ballesteros, F.J. Herranz, O. Ragnisco, and D. Riglioni).
A new exactly solvable quantum model in N dimensions, Phys. Lett. A 375 (2011) 1431–1435 (with A. Ballesteros, F.J. Herranz, O. Ragnisco, and D. Riglioni).
Superintegrable oscillator and Kepler systems in spaces of nonconstant curvature via the Stäckel transform, SIGMA 7 (2011) 048 (with A. Ballesteros, F.J. Herranz, O. Ragnisco, and D. Riglioni).
Quantum mechanics on spaces of nonconstant curvature: the oscillator problem and superintegrability, Ann. Phys. 326 (2011) 2053–2073 (with A. Ballesteros, F.J. Herranz, O. Ragnisco, and D. Riglioni).
Global causal propagator for the Klein–Gordon equation on a class of supersymmetric AdS backgrounds, Adv. Theor. Math. Phys. 14 (2010) 1147–1181 (with N. Kamran).
Level density of spin chains of Haldane–Shastry type, Phys. Rev. E 82 (2010) 051117(6) (with F. Finkel and A. González-López).
Existence and vanishing set of inverse integrating factors for analytic vector fields, Bull. London Math. Soc. 41 (2009) 1112–1124 (with D. Peralta-Salas).
Green’s function for the Hodge Laplacian on some classes of Riemannian and Lorentzian symmetric spaces, Comm. Math. Phys. 290 (2009) 105–127 (with N. Kamran).
Spin chains of Haldane–Shastry type and a generalized central limit theorem, Phys. Rev. E 79 (2009) 060105R(4) (with F. Finkel and A. González-López).
Superintegrability on N-dimensional curved spaces: central potentials, centrifugal terms and monopoles, Ann. Phys. 234 (2009) 1219–1233 (with A. Ballesteros, F.J. Herranz, and O. Ragnisco).
Critical points and level sets in exterior boundary problems, Indiana Univ. Math. J. 58 (2009) 1947–1970 (with D. Peralta-Salas).
Hamiltonian systems admitting a Runge–Lenz vector and an optimal extension of Bertrand’s theorem to curved manifolds, Comm. Math. Phys. 290 (2009) 1033–1049 (with A. Ballesteros, F.J. Herranz, and O. Ragnisco).
A symmetry result for the p-Laplacian in a punctured manifold, J. Math. Anal. Appl. 354 (2009) 619–624 (with D. Peralta-Salas).
Symmetry for an overdetermined boundary problem in a punctured domain, Nonlinear Anal. 70 (2009) 1080–1086 (with D. Peralta-Salas).
Morse-type inequalities for dynamical systems and the Witten Laplacian, J. Differential Equations 244 (2008) 2804–2819 (with D. Peralta-Salas).
A maximally superintegrable system on an n-dimensional space of nonconstant curvature, Phys. D 237 (2008) 505–509 (with A. Ballesteros, F.J. Herranz, and O. Ragnisco).
Bertrand spacetimes and the oscillator and Kepler–Coulomb potentials, Class. Quant. Grav. 25 (2008) 165005 (with A. Ballesteros, F.J. Herranz, and O. Ragnisco).
A novel quasi-exactly solvable spin chain with nearest-neighbors interactions, Nucl. Phys. B 789 (2008) 452–482 (with F. Finkel, A. González-López, and M.A. Rodríguez).
Partially solvable spin chains and QES spin models, J. Nonlinear Math. Phys. 15 (2008) 155–165 (with F. Finkel, A. González-López, and M.A. Rodríguez).
N-dimensional sl(2)-coalgebra spaces with non-constant curvature, Phys. Lett. B 652 (2007) 376–383 (with A. Ballesteros, F.J. Herranz, and O. Ragnisco).
Geometrical and topological aspects of Electrostatics on Riemannian manifolds, J. Geom. Phys. 57 (2007) 1679–1696 (with D. Peralta-Salas).
Exchange operator formalism for N-body spin models with near-neighbours interactions, J. Phys. A 40 (2007) 1857–1883 (with F. Finkel, A. González-López, and M.A. Rodríguez).
Quasi-exactly solvable N-body spin Hamiltonians with short-range interaction potentials, SIGMA 2 (2006) 73 (with F. Finkel, A. González-López, and M.A. Rodríguez).
Classical and quantum integrability of Hamiltonians without scattering states, Theor. Math. Phys. 148 (2006) 1086–1099 (with D. Peralta-Salas).
The fermion density operator in the droplet bosonization picture, Nucl. Phys. B 751 (2006) 376–391 (with A.P. Polychronakos).
Haldane–Shastry spin chains of BCN type, Nucl. Phys. B 707 (2005) 553–576 (with F. Finkel, A. González-López, and M.A. Rodríguez).
A Haldane–Shastry spin chain of BCN type in a constant magnetic field, J. Nonlinear Math. Phys. 12 (2005) 253–265 (with F. Finkel, A. González-López, and M.A. Rodríguez).
Solvable scalar and spin models with near-neighbors interactions, Phys. Lett. B 605 (2005) 214–222 (with F. Finkel, A. González-López, and M.A. Rodríguez).