Francisco de la Hoz Méndez (Patxi)
Francisco de la Hoz Méndez (Patxi)
Personal data:
Date and place of birth: March 27th, 1979, Bilbao (Spain)
Current position (from June 1st, 2011):
Associate Professor (in Spanish, Profesor Agregado de Universidad). It is a tenured, non-civil servant position equivalent to Profesor Titular de Universidad in the Basque Country.
Address:
University of the Basque Country (UPV/EHU)
Faculty of Science and Technology
Barrio Sarriena S/N
48940 Leioa (Spain)
Office Phone: +34 94 601 7896
E-mail: francisco.delahoz AT ehu.eus (replace AT with @)
ORCID iD: 0000-0001-7052-0229
Scopus Author ID: 24075211300
ResearcherID: R-1396-2018
Mendeley profile: https://www.mendeley.com/profiles/francisco-de-la-hoz/
Scientific Production Portal of the University of the Basque country
Academic background:
October, 2016: Grado en Ingeniería Informática (four-year university degree in Computer Engineering) from UNED
December, 2007: Ph. D. in Mathematics from UPV/EHU
December, 2004: Diploma of Advanced Studies in Mathematical Analysis from UPV/EHU
June, 2004: Ingeniería Técnica en Informática de Sistemas (three-year university degree in Computer Engineering) from UNED
June, 2002: Licenciatura en Matemáticas (five-year university degree in Mathematics) from UPV/EHU
Research fields:
Fractional numerical analysis
Hypergeometric functions
Matrix numerical analysis
Pseudo-spectral methods
Vortex filament motion
Vortex patch motion
Water waves
Stochastic Differential Equations
Ph. D. Thesis:
Spanish language version: Estudio numérico de ciertos flujos geométricos que desarrollan singularidades en tiempo finito. ISBN: 978-84-9860-112-1.
Basque language version: Denbora finituan singulartasunak garatzen dituzten zenbait fluxu geometrikoren zenbakizko azterketa. ISBN: 978-84-8438-172-3.
Publications in journals with impact factor (JCR):
J. Cayama, C. M. Cuesta, F. de la Hoz, C. J. García-Cervera, A fast convolution method for the fractional Laplacian in R, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 119:80 (2025), 1-45.
F. de la Hoz, S. Iakunin, A study of the reconnection of antiparallel vortices in the infinitely thin case and in the finite thickness case, Physica D: Nonlinear Phenomena 481 (2025), 134782.
C. M. Cuesta, F. de la Hoz, I. Girona, Numerical Approximation of Riesz-Feller Operators on R, Journal of Computational and Applied Mathematics 454 (2025), 116194.
F. Chamizo, F. de la Hoz, Regular Polygonal Vortex Filament Evolution and Exponential Sums, Acta Applicandae Mathematicae 194:8 (2024), 1-8.
C. M. Cuesta, F. de la Hoz, I. Girona, Numerical computation of the half Laplacian by means of a fast convolution algorithm, Electronic Transactions on Numerical Analysis 60 (2024), 59-98.
F. de la Hoz, S. Kumar, L. Vega, Vortex Filament Equation for a Regular Polygon in the Hyperbolic Plane, Journal of Nonlinear Science 32:9 (2022), 1-34.
J. Cayama, C. M. Cuesta, F. de la Hoz, A Pseudospectral Method for the One-Dimensional Fractional Laplacian on R, Applied Mathematics and Computation 389 (2021), 125577.
J. Cayama, C. M. Cuesta, F. de la Hoz, Numerical Approximation of the Fractional Laplacian on R Using Orthogonal Families, Applied Numerical Mathematics 158 (2020), 164-193.
F. de la Hoz, S. Kumar, L. Vega, On the Evolution of the Vortex Filament Equation for Regular M-Polygons with Nonzero Torsion, SIAM Journal on Applied Mathematics 80:2 (2020), 1034-1056.
F. de la Hoz, L. Vega, On the Relationship Between the One-Corner Problem and the M-Corner Problem for the Vortex Filament Equation, Journal of Nonlinear Science 28 (2018), 2275-2327.
F. de la Hoz, Z. Hassainia, T. Hmidi, J. Mateu, An analytical and numerical study of steady patches in the disc, Analysis & PDE 9:7 (2016), 1609-1670.
F. de la Hoz, T. Hmidi, J. Mateu, J. Verdera, Doubly connected V-states for the planar Euler equations, SIAM Journal on Mathematical Analysis 48:3 (2016), 1892-1928.
F. de la Hoz, Z. Hassainia, T. Hmidi, Doubly connected V-states for the generalized surface quasi-geostrophic equations, Archive for Rational Mechanics and Analysis 220:3 (2016), 1209-1281.
F. de la Hoz, C. M. Cuesta, A pseudo-spectral method for a non-local KdV-Burgers equation posed on R, Journal of Computational Physics 311 (2016), 45-61.
F. de la Hoz, F. Vadillo, Numerical Simulations of Time-dependent Partial Differential Equations, Journal of Computational and Applied Mathematics 295 (2016), 175-184.
F. de la Hoz, A. Doubova, F. Vadillo, Persistence-time Estimation for some Stochastic SIS Epidemic Models, Discrete and Continuous Dynamical Systems - Series B 20:9 (2015), 2933-2947.
F. de la Hoz, L. Vega, The Vortex Filament Equation as a Pseudorandom Generator, Acta Applicandae Mathematicae 138:1 (2015), 135-151.
F. de la Hoz, L. Vega, Vortex filament equation for a regular polygon, Nonlinearity 27:12 (2014), 3031-3057.
F. de la Hoz, F. Vadillo, The Solution of Two-Dimensional Advection-Diffusion Equations via Operational Matrices, Applied Numerical Mathematics 72 (2013), 172-187.
F. de la Hoz, F. Vadillo, A Sylvester-Based IMEX Method via Differentiation Matrices for Solving Nonlinear Parabolic Equations, Communications in Computational Physics 14:4 (2013), 1001-1026.
F. de la Hoz, F. Vadillo, A mean extinction-time estimate for a stochastic Lotka–Volterra predator–prey model, Applied Mathematics and Computation 219:1 (2012), 170-179.
F. de la Hoz, F. Vadillo, Numerical simulation of the N-dimensional sine-Gordon equation via operational matrices, Computer Physics Communications 183:4 (2012), 864-879.
F. de la Hoz, F. Vadillo, An integrating factor for nonlinear Dirac equations, Computer Physics Communications 181:7 (2010), 1195-1203.
M. A. Fontelos, F. de la Hoz, Singularities in Water Waves and the Rayleigh-Taylor Problem, Journal of Fluid Mechanics 651 (2010), 211-239.
F. de la Hoz, L. Vega, C. J. García-Cervera, A numerical study of the self-similar solutions of the Schrödinger Map, SIAM Journal on Applied Mathematics 70:4 (2009), 1047-1077.
F. de la Hoz, Numerical study of a flow of regular planar curves that develop singularities at finite time, SIAM Journal on Applied Mathematics 70:1 (2009), 279-301.
F. de la Hoz, F. Vadillo, A numerical simulation for the blow-up of semi-linear diffusion equations, International Journal of Computer Mathematics 86:3 (2009), 493-502.
F. de la Hoz, M. A. Fontelos, The structure of singularities in nonlocal transport equations, Journal of Physics A: Mathematical and Theoretical 41 (2008), 185204 (12pp).
F. de la Hoz, M. A. Fontelos, L. Vega, The Effect of Surface Tension on the Moore Singularity of Vortex Sheet Dynamics, Journal of Nonlinear Science 18:4 (2008), 463-484.
F. de la Hoz, F. Vadillo, An exponential time differencing method for the nonlinear Schrödinger equation, Computer Physics Communications 179:7 (2008), 449-456.
F. de la Hoz, Self-similar solutions for the 1-D Schrödinger map on the hyperbolic plane, Mathematische Zeitschrift 257:1 (2007), 61-80.
Submitted publications:
F. de la Hoz, P. Muniain, Numerical approximation of Caputo-type advection-diffusion equations in one and multiple spatial dimensions via shifted Chebyshev polynomials, submitted (2025).
F. de la Hoz, P. Muniain, Numerical approximation of Caputo-type advection-diffusion equations via Sylvester equations, arXiv:2501.09180 (2025).
C. M. Cuesta, F. de la Hoz, A non-recursive Schur-Decomposition Algorithm for $N$-Dimensional Matrix Equations, arXiv:2412.15840 (2024).
Publications in journals without impact factor:
F. de la Hoz, L. Vega, The Evolution of the Local Induction Approximation for a Regular Polygon, ESAIM: PROCEEDINGS AND SURVEYS, September 2014, Vol. 45, p. 447-455.
F. de la Hoz, A matrix-based numerical method for the simulation of the two-dimensional sine-Gordon equation, ESAIM: PROCEEDINGS, March 2012, Vol. 35, p. 216-221.
Book chapters:
F. de la Hoz, Z. Hassainia, T. Hmidi, Doubly connected V-states for the generalized surface quasi-geostrophic equations, Evolution equations: long time behavior and control, 90-117, London Mathematical Society Lecture Note Series (439), Chapter 4, Cambridge University Press, Cambridge, 2017.
Other publications:
F. de la Hoz, S. Kumar, L. Vega, Vortex Filament Equation for a regular polygon in the Hyperbolic plane, Proceedings of the CEDYA + CMA 2017, Cartagena (Spain), 2017, pp. 239-243. ISBN 978-84-944402-1-2.
F. de la Hoz, L. Vega, On the Complete Determination of the Evolution of the Vortex Filament Equation for Regular Planar Polygons, Proceedings of the CEDYA + CMA 2017, Cartagena (Spain), 2017, pp. 379-384. ISBN 978-84-944402-1-2.
F. de la Hoz, Análisis numérico de soluciones autosemejantes de un flujo dispersivo de curvas planas, Proceedings of the Proceedings of the CEDYA + CMA 2007, Seville (Spain), 2007. ISBN 978-84-690-7182-3.
F. de la Hoz, Soluciones numéricas de la Schrödinger Map, Proceedings of the Primer Congreso Internacional de Matemáticas en Ingeniería y Arquitectura (M&I 2007), Universidad Politécnica de Madrid, Madrid (Spain), 2007, pp. 467-470. ISBN: 978-84-7493-381-9.
Lectures in congresses:
F. de la Hoz, A Quaternion-Based Approach to Determining the Angle Between Adjacent Sides in the Evolution of Regular Polygons Under the Vortex Filament Equation, Workshop "Mathematical Modelling in Superfluids, Mojacar (Spain), 2025.
F. de la Hoz, Numerical Approximation of Riesz-Feller Operators on the real line, 9th European Congress of Mathematics (ECM), Sevilla (Spain), 2024.
F. de la Hoz, A quaternion approach to determine the angle between adjacent sides in the evolution of regular polygons under the vortex filament equation, CEDYA + CMA 2024, Leioa (Spain), 2024.
F. de la Hoz, A second-order fast-convolution method for the fractional Laplacian, Congreso Bienal de la Real Sociedad Matemática Española, Pamplona (Spain), 2024.
F. de la Hoz, Understanding the Evolution of the Vortex Filament Equation for Initial Polygonal Data, Workshop on Vortex Filaments, The Fields Institute for Research in Mathematical Sciences, Toronto (Canada), 2020.
F. de la Hoz, On the Evolution of the Vortex Filament Equation for More General Polygons, 72nd Workshop: New Trends in Propagation of Linear and Nonlinear Wave Phenomena, International School of Mathematics “Guido Stampacchia”, Erice, Sicily (Italy), 2019.
F. de la Hoz, Recent Developments on the Vortex Filament Equation for Regular Polygons, CEDYA + CMA 2017, Cartagena (Spain), 2017.
F. de la Hoz, Bortizitate harizpiaren ekuazioaren eboluzioa hasierako datu izkinadunetarako, Matematikari Euskaldunen II. Topaketak, Eibar (Spain), 2016.
F. de la Hoz, The Evolution of the Vortex Filament Equations for a Regular Polygon, SIAM Conference on Analysis of Partial Differential Equations, Scottsdale (Arizona, USA), 2015.
F. de la Hoz, On the generation of random numbers by means of the vortex filament equation, First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI, Leioa (Spain), 2014.
F. de la Hoz, The Evolution of the Local Induction Approximation for a Regular Polygon, Schrödinger Equations and Applications Workshop, CIRM, Marseille (France), 2014.
F. de la Hoz, On the evolution of the binormal flow for a regular polygon, The Second BCAM Workshop on Computational Mathematics, BCAM, Bilbao (Spain), 2013.
F. de la Hoz, A Hermite-Pseudospectral Method for the Two-Dimensional Semilinear Parabolic Equation, CANUM 2012, Superbesse (France), 2012.
F. de la Hoz, Singularities in Fluid Dynamics, Workshop for Young Researchers in Mathematics, Constanţa (Romania), 2012.
F. de la Hoz, A Matrix-based Method for the N-dimensional Sine-Gordon Equation, SMAI 2011, Guidel, Bretagne (France), 2011.
F. de la Hoz, Two-Dimensional Advection-Diffusion Equations, Differentiation Matrices and Sylvester Systems, SANUM 2011, Stellenbosch (South Africa), 2011.
F. de la Hoz, Singularities in Hydrodinamics, Euskadi-Kyushu 2011, BCAM, Bilbao (Spain), 2011.
F. de la Hoz, Some topics concerning the evolution of vortex sheets, Première rencontre des mathématiciens de l’UPPA et de l’UPV/EHU, Anglet (France), 2010.
F. de la Hoz, Numerical Study of a Geometric Flow of Curves that Develop Singularities in Finite Time, ICM 2010, Hyderabad (India), 2010.
F. de la Hoz, Exponential Time Differencing Methods for Nonlinear Evolution PDEs, DSPDEs'10, Barcelona (Spain), 2010.
F. de la Hoz, L. Vega, Some geometric models for vortex dynamics, New directions in Continuum Mechanics: on the interplay among Mathematics, Mechanics and Physics, Castro-Urdiales (Spain), 2008.
F. de la Hoz, Going beyond Moore's singularity: a numerical study of the regularizing effect of surface tension on vortex sheet dynamics, CANUM 2008, Saint Jean de Monts (France), 2008.
F. de la Hoz, Soluciones numéricas de la Schrödinger Map, M&I 2007, Madrid (Spain), 2007. Published in the proceedings of the congress. ISBN 978-84-7493-381-9.
F. de la Hoz, Análisis numérico de soluciones autosemejantes de un flujo dispersivo de curvas planas, CEDYA + CMA 2007, Seville (Spain), 2007. Published in the proceedings of the congress. ISBN 978-84-690-7182-3.
F. de la Hoz, Self-similar Solutions for the 1-D Schrödinger Map on the Hyperbolic Plane, ICM 2006, Madrid (Spain), 2006.
Posters presented in congresses:
F. de la Hoz, The evolution of the vortex filament equation for a regular polygon, Cádiz Numérica 2013, Cádiz (Spain), 2013.
F. de la Hoz, The evolution of the vortex filament equation for a regular polygon, SMAI 2013, Seignosse le Penon (France), 2013.
F. de la Hoz et al., Mathematical Analysis and Applications. Numerical Analysis, III Jornadas de Investigación de la Facultad de Ciencia y Tecnología, Leioa (Spain), 2012. Published in the proceedings of the congress. ISBN: 978-84-9860-853-3
F. de la Hoz et al., Mathematical foundations of statistical mechanics and dispersive equations in quantum mechanics, II Jornadas de Investigación de la Facultad de Ciencia y Tecnología, Leioa (Spain), 2010.
F. de la Hoz et al., Numerical methods in mathematical problems, II Jornadas de Investigación de la Facultad de Ciencia y Tecnología, Leioa (Spain), 2010.
F. de la Hoz, Self-Similar Solutions of the Localized Induction Approximation: A Numerical Study, II i-MATH School on Numerical Solutions of Partial Differential Equations, Málaga (Spain), 2010.
F. de la Hoz et al., Grupo de análisis matemático y aplicaciones. Línea de investigación: análisis numérico, I Jornadas de Investigación de la Facultad de Ciencia y Tecnología, Leioa (Spain), 2008. Published in the proceedings of the congress. ISBN: 978-84-9860-118-3.
F. de la Hoz et al., Grupo: Análisis Matemático y Aplicaciones. Física Matemática, I Jornadas de Investigación de la Facultad de Ciencia y Tecnología, Leioa (Spain), 2008. Published in the proceedings of the congress. ISBN: 978-84-9860-118-3.
Undergraduate books:
N. Barrado, F. de la Hoz, J. L. Carro, I. Lecubarri, Kalkulua. Azterketa Ariketak, 2013.
F. de la Hoz, N. Barrado, J. L. Carro, I. Lecubarri, Kalkulua. Teoria eta Ariketak, 2010. ISBN: 978-84-614-3116-8.
F. de la Hoz, J. L. Carro, I. Lecubarri, E. Martínez, Ingeniaritzaren Oinarri Matematikoak I. Teoria eta Ariketak, 2009. ISBN: 978-84-613-6790-0.
Aranese language:
Francisco de la Hoz, Jusèp Loís Sans Socasau, Diccionari aranés - español, Institut d'Estudis Aranesi - Acadèmia Aranesa dera Lengua Occitana, 2024. ISBN: 978-84-09-64368-4.
Awards:
Extraordinary Ph. D. Award (in Spanish, Premio Extraordinario de Doctorado).
1st Koldo Mitxelena Prize in Experimental Sciences (in Basque, I. Koldo Mitxelena Saria, Zientzia Esperimentaletan).
Hobbies:
Linguistics & World Languages.
Links:
Updated:
June 22nd, 2025.