Alejandro joined NU as an Assistant Professor in the Department of Mathematics the summer of 2016. He is from Tenerife (Spain) where he obtained the PhD degree in Mathematics in 2014 at the University of La Laguna. Later he spent two years in Sweden with a PostDoc position at Uppsala University. His research spans a broad area within Harmonic Analysis and its applications to Partial Differential Equations. Particularly, he is interested in nonlinear dispersive PDEs, oscillatory integrals, Maxwell’s equations, well-posedness of low regularity parabolic equations and singular operators associated with general Laplacians. Lately, he has been attracted by novel approaches for solving PDEs: by means of Neural Networks and Quantum Computing.

Personal Webpage: https://sites.google.com/site/ajcastroajcastro/home

A.J. Castro, K. Jabbarkhanov, L. Zhapsarbayeva
The Nonlinear Schrödinger-Airy equation in weighted Sobolev spaces,
Nonlinear Anal. Theory Methods Appl. 223 (2022), 113068.

A.J. Castro, A. Israelsson, W. Staubach,
Regularity of Fourier integral operators with amplitudes in general Hörmander classes,
Anal. Math. Phys. 11 (2021), 1-54.

D. O. Da Silva, A.J. Castro,
Global well-posedness for the nonlinear wave equation in analytic Gevrey spaces,
J. Differ. Equ. 275 (2021), 234-249.

A. Assaubay, A.J. Castro, A.A. Valido,
Wigner instability analysis of the damped Hirota equation,
Physica D 411 (2020), 132587.

A.J. Castro, S. Rodríguez-López, W. Staubach,
Transference of local to global L2 maximal estimates for dispersive partial differential equations,
J. Math. Anal. Appl. 471 (2019), 411-422.

A.J. Castro, S. Rodríguez-López, W. Staubach,
L^2-solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with time-independent Hölder-continuous coefficients,
Trans. Amer. Math. Soc. 370 (2018), 265-319.

J.J. Betancor, A.J. Castro, J.C. Fariña, L. Rodríguez-Mesa,
Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces,
J. Math. Anal. Appl. 447 (2017), 32-75.

A.J. Castro, K. Nyström, O. Sande,
Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients,
Calc. Var. Partial Differ. Equ. 55 (2016), 1-49.

A.J. Castro, T. Hytönen,
Bounds for partial derivatives: necessity of UMD and sharp constants,
Math. Z. 282 (2016), 635-650.

J.J. Betancor, A.J. Castro, J.C. Fariña, L. Rodríguez-Mesa,
Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions,
J. Math. Anal. Appl. 431 (2015), 440-470.

J.J. Betancor, A.J. Castro, P.R. Stinga,
The fractional Bessel equation in Hölder spaces,
J. Approx. Theory 184 (2014), 55-99.

J.J. Betancor, A.J. Castro, J. Curbelo, L. Rodríguez-Mesa,
Characterization of UMD Banach spaces by imaginary powers of Hermite and Laguerre operators,
Complex Anal. Oper. Theory 7 (2013), 1019-1048.

J.J. Betancor, A.J. Castro, J. Curbelo, J.C. Fariña, L. Rodríguez-Mesa,
gamma-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces,
J. Funct. Anal. 263 (2012), 3804-3856.

J.J. Betancor, A.J. Castro, J. Curbelo,
Spectral multipliers for multidimensional Bessel operators,
J. Fourier Anal. Appl. 17 (2011), 932-975.

MATH 161 Calculus I
MATH 162 Calculus II
MATH 263 Calculus III
MATH 273 Linear Algebra with Applications
MATH 274 Introduction to Differential Equations
MATH 351 Numerical Methods with Applications
MATH 361 Real Analysis I
MATH 471 Nonlinear Differential Equations
MATH 480 Complex Analysis
MATH 481 Partial Differential Equations
MATH 482 Fourier Analysis
MATH 676 Advanced Partial Differential Equations with Applications
MATH 701 Real Analysis
MATH 702 Functional Analysis with Applications