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Luis Vega González

Group Leader. BCAM-UPV/EHU Professor

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T +34 946 567 842
F +34 946 567 842
E lvega@bcamath.org

Information of interest

My research is mainly focused in the interplay of Fourier Analysis and Partial Differential Equations of Mathematical Physics. More recently on fluid mechanics and turbulence. Concretely in the so called Localized Induction Approximation, also known as the binormal curvature flow (BF),  for the evolution of vortex filaments and the relevance of the presence of corners in the filament. The results concerning regular polygons seem to me quite striking. Motivated by a numerical experiment done by D. Smets, and together with F. De La Hoz, we established in 2014 a numerical connection between the trajectory followed by a corner of, say an equilateral triangle, and a classical analytical problem  that goes back at least to Riemann: the existence of continuous functions which are no where differentiable. Very recently (arXiv:2007.07184), and in collaboration with V. Banica, we have proved analytically that this connection is indeed true. 

Right now I am also working together with N. Arrizabalaga and A. Mas, on relativistic and non-relativistic equations with singular electromagnetic potentials. The singularities of the potentials are critical from the point of view of the scaling symmetry. In the relativistic setting we consider perturbations of Dirac equation given by singular measures supported on smooth hyper-surfaces. This mathematical problem is closely related to a relevant question in physics, that of the optimal confinement of relativistic quantum particles.

Finally I continuous working on the deep connection between uncertainty principles, that are easily described using the Fourier transform, and lower bounds for solutions of linear and non-linear dispersive equations. This is a topic that I started with L. Escauriaza, Carlos E. Kenig and G. Ponce more than 10 years ago and from which very fruitful branches have emerged. For example, one of the first consequences we obtained using these lower bounds, was that a compact perturbation of a solitary wave or soliton of the Korteweg-De Vries (KdV) equation instantaneously destroys its exponential decay. KdV is a simplified local model about the dynamics of the frontier of a fluid. In particular, it describes with very high accuracy the propagation of a wave along a narrow and sallow channel. However, when the depth is big so that it can be considered close to be infinite the local approximation is too rough and non-local models as the Benjamin-Ono equation has to be considered. It turns out that the answer to the corresponding question requires completely different techniques that are closer to those developed with A. Fernández-Bertolin for the discrete laplacian and with L. Roncal and D. Stan for the fractional laplacian.

  • CEX2021001142-S acredited as "Centro de Excelencia Severo Ochoa". MINECO, Spain. 01/01/2023 - 31/12/2026. Total amount: 4.000.000€
  • SEV-2017-0718 acredited as "Centro de Excelencia Severo Ochoa". MINECO, Spain. 01/07/2018 - 30/06/2022. Total amount: 4.000.000€
  • IT-1247-19 Análisis matemático y numérico de algunas ecuaciones en derivadas parciales y sus aplicaciones. Basque Government, Spain. 01/01/2019 - 31/12/2021. Total amount: 326.500€
  • PGC2018-094522-B-I00, Análisis matemático y numérico de algunas ecuaciones en derivadas parciales y sus aplicaciones. Ministry of Science and Innovation, Spain.01/01/2019 - 31/12/2021. Total amount: 125.780€
  • 669689-HADE-Harmonic Analysis and Differential Equations: new challenges. ERC-EA European Research Council Executive Agency (H2020). 01/12/2015-30/11/2021. Total amount: 1.672.103€
  • SEV-2013-0323 accredited as "Centro de de Excelencia Severo Ochoa-Severo Ochoa Excellence Center". MINECO, Spain 01/07/2014-30/06/2018. Total amount: 4.000.000€
  • IT-641-13 Mathematical Physics, mathematical Analysis and PDEs and Numerical Analysis. Basque Government, Spain. 01/01/2013-31/12/2018. Total amount: 302.000€
  • MTM2014-53145-P Analisis teórico y numérico de ecuaciones de evolución. MINECO, Spain 01/01/2015-31/12-2017. Total amount: 102.000€
  • BERC.2014-2017 Centros de Investigación Básica y de Excelencia. Basque Government 01/01/2014-01/12/2017

News 

Dissemination activities

Date Title Place
2023-06-16 Desingularization of the Biot-Savart integral and the Localised Induction Approximation (LIA) Bilbao
2023-05-24 Blow-up for the 1d cubic NLS and related systems IHES, Conference in honor of F-Merles. Bures sure Yvette, France
2023-03-13 New Conservations Laws and Energy Cascade for 1d Cubic NLS University of Cambridge, Depart. of Mathematics
2022-03-17 Matemáticas y Turbulencia Universidad Politécnica de Madrid
2022-08-08 Intermittency and the Talbot effect Université Lyon
2021-11-01 Lower Bounds fro Oscilatory Integrals Depart. of Mathematics, Brown University, RI, USA
2021-10-18 Fluctuations of ∂-moments free Schrödinger equation ICERM, Brown University, RI, USA
2021-09-17 Riemmann's non-differentable function and the binormal curvature flow ICERM, Brown University, RI, USA
2021-08-02 Riemmann's non-differentable function and the binormal curvature flow Virtual - Inst. Matem Pura e Appl (IMPA), Rio de Janeiro, Brasil
2021-05-05 Riemmann's non-differentable function and the binormal curvature flow Virtual - Ecole Normale Superieure de Lyon
2021-04-12 Riemmann's non-differentable function and the binormal curvature flow Virtual - Math. Science Res Int. (MSRI), Berkeley, USA
2021-01-08 Riemmann's non-differentable function and the binormal curvature flow Virtual - NYU Abu Dhabi
2020-12-08 Riemmann's non-differentable function and the binormal curvature flow Virtual - One World PDE Seminar, Portugal
2020-10-28 Riemmann's non-differentable function and the binormal curvature flow Virtual - Fields Institute, Toronto
2020-10-24 Riemmann's non-differentable function and the binormal curvature flow Toronto
2020-10-20 Riemmann's non-differentable function and the binormal curvature flow Virtual - Building Bridges - Academia Europea Barcelona Knowledge Hub
2020-09-10 The binormal flow, the Talbot effect, and non-circular jets PDE Zoom-seminar, Shanghai
2019-02-08 Lower bounds for Schrödinger evolutions UCSB
2017-01-27 Shell interactions for dirac operators. an isoperimetric-type Inequality Zaragoza
2016-12-14 Singular solutions of the Binormal Flow: transfer of energy and momentum Valdivia, Chile
2016-10-20 The Talbot Effect and The Ecolution of Vortex Filaments MSRI, USA
2016-08-23 Shell interactions for Dirac operators: An isoperimetric-type inequality Sapporo, Japan
2016-05-09 Las matemáticas en la hora de la innovación Periódico "El Correo"
2015-06-25 Some Remarks about the Uncertainty Principle UAM, Spain
2015-06-17 The Vortex filament equation for a regular polygon and the Talbot effect https://www.youtube.com/watch?v=Z1gXJKLw2Fo
2014-11-13 El tablero de Galton Facultad de Ciencia y Tecnología de la UPV/EHU
2014-09-21 Shell interactions for Dirac operators: selfadjointeness, point spectrum, and confinement Chicago, USA
2012-11-02 Las matemáticas están para usarlas UPV/EHU, Spain
2011-10-19 Asymptotic Lower Bounds for Solutions to Dispersive Equations Mexico DF
2011-09-01 A New Approach to HArdy's Uncertainty Principle Lexington
2011-06-14 Unidad de Biomedicina Cuantitativa BioCruces, Barakaldo
2011-06-10 A Geometric Description of the Formation of Singularities in the Binormal Flow ETH Zurich
2011-02-01 ¿Matemáticas? Sí, gracias.  Periódico "El Correo"
2010-06-01 Oscilatory Integrals and Euler Equations CSIC Madrid
2006-01-03 The initial value problem for non-linear Shrödinger equations ICM Madrid

 

  • Ministry of Science and Technology, Spain - PI of the Strategic Network of Mathematics - Scientific Committee 2020
  • International Congress of Industrial and Applied Mathematics (ICIAM) - Officer - Scientific Committees - October 2019 - December 2019
  • European Academy of Sciences, Division of Mathematics - Officer - Scientific Committee - March 2019 - March 2023
  • Journal Serie A Matemáticas, Spanish Academy of Sciences - General Editor - 2018 
  • L'institut Universitaire de France (IUF) - Member of the Comission - Scientific Committees - 2016-2017
  • Asociación ICIAM Valencia 2019 - Vice-presicent - Scientific Committees - 2014-2019
  • Basque Center for Applied Mathematics (BCAM) - Scientific Director - Scientific Committee 2013-2019
  • Spanish Candidacy for ICIAM Valencia 2019 - Defensor of the bid - Scientific Committee - 2013
  • Journal Serie A Matemáticas, Spanish Academy of Sciences - Member of the Editorial Boards - 2013 
  • Training and Research Unit of Mathematics and Applications (UPV/EHU) - Director - Scientific Committee - 2012-2013
  • Spanish Candidacy for ICIAM Valencia 2019 - Defensor of the prebid - Scientific Committee - 2012
  • Mathematical European Week-end, Bilbao - Chair of the Program Committee - Scientific Committee - 2011
  • Linköping University, Sweden - Jury Member - Scientific Committee - 2011
  • Department of Quantitative Biomedicine, Biocruces Research Institute - Director - Scientific Committee - 2011
  • Academy of Finland - Panel member of the research projects - Scientific Committee - 2010
  • Spanish Royal Mathematical Society (RSME) - Vice-president - Scientific Committee - 2009-2012
  • ICIAM - Member of the Executive Board -  Scientific Committee - 2008-2013
  • University of the Basque Country/Universidad del País Vasco/Euskal Herriko Unibertsitatea (UPV/EHU) - Director of the PhD Programme in Mathematics - Scientific Committee - 2007 - 2013
  • Inter-university master program in Applied Mathematics (UPV/EHU and another four universities) - Director - Scientific Activities - 2006-2012
  • Habilitation and PhD theses at several foreign universities - Jury Member - Scientific Committee - 2004
  • Medalla Real Sociedad Matemática Española (RSME) 2023 - Spanish Royal Mathematical Society (RSME) Medal 2023, Spain, 2023 
  • Severo Ochoa Excellence Accreditation, BCAM, 2023-2026
  • National Research Award "Julio Rey Pastor" 2021, in Mathematics and Information and Communication Technologies
  • Severo Ochoa Excellence Accreditation, BCAM, 2018-2022
  • Severo Ochoa Excellence Accreditation, BCAM, 2014-2018
  • ERC-Advance Grant, European Research Council, Brussels, Belgium, 2015-2021
  • Elected member of the Real Academia de Ciencias, Spain, 2018
  • Member of the European Academy of Sciences; European Academy of Sciences, Liege, Belgium, 2014
  • Blaise Pascal Medal, European Academy of Sciences, Liege, Belgium, 2014
  • Le Prix La Recherche, Mathematiques, France, 2014
  • Member of the "Real Academia de Ciencias Exactas, Físicas y Naturales-RAC", Spain, 2013
  • Fellow of the American Mathematical Society, Inaugural Class, 2012
  • Premio Euskadi de Investigación - Euskadi Research Prize, Basque Government, Spain, 2012
  • Highly Cited Researcher, ISI Web os Science, 2004
  • Iberdrola grant for Visiting Fellows, Spain, 1997
  • National Science Foundation grant, USA, 1989-90