Emeritus Professor
formerly Full Professor of Applied Mathematics
Department of Mathematics
Campus de Cantoblanco, 28049 Madrid
juanluis.vazquez at uam.es

Exactas, Físicas y Naturales

Juan Luis Vázquez Suárez ./englflag.gif  Version in Spanish / Versión en español

List of Mathematical Publications 1980-1999   2000-2024 My books
Mathematical and expository writing Courses, books and notes

Research Interests

Differential equations, especially nonlinear partial differential equations, and their applications to Physics and Engineering.   Diffusion equations, filtration equations in porous media.   Mathematical study of processes with free boundaries and change of phase.   Special solutions, selfsimilarity and asymptotical methods.   Blow-up problems and singularities.  Nonlocal diffusion and fractional Laplacian operators.   PDEs and Riemannian Geometry.   Entropy methods and functional inequalities.            Personal CV

Mathematical activities, events and writings, 2024

* Summer School UIMP 2024 in Mathematics.   Title: The Laplacian and Beyond. Celebrating the Mathematics of Luis Caffarelli. The school will be held from 22 to 26 July, 2024 at the Magdalena Palace of UIMP, the Universidad Internacional Menéndez Pelayo, in Santander, Spain. Organizers: Matteo Bonforte (UAM-ICMAT), Juan Luis Vázquez (UAM-RAC). Poster Announcement.

Mathematical activities, events and writings, 2023

* EURO-JAPANESE Conference on Nonlinear Diffusions,   weekly event   held in Madrid from October 16 to 20, at the ICMAT Institute as part of the 2023 Thematic Period PDEs ICMAT-UAM. Organizers: Goro Akagi (Tohoku University), Matteo Bonforte (UAM-ICMAT), Kazuhiro Ishige (University of Tokyo), Juan Luis Vázquez (UAM-RAC). Conference Poster.

* The Abel Prize 2023 has been awarded to Luis Caffarelli by the Norwegian Academy of Sciences and Letters. See announcement in Oslo on March 22, 2023, and article of the Norwegian Academy about Luis Caffarelli. Hereby the article by JLV in Spanish about Luis Caffarelli, appeared in Bulletín 798 of RSME, the Royal Spanish Mathematical Society, pages 5-7.   Next, article in English   appeared in IMTech Newsletter 2023, UPC Barcelona, pages 13-14.
  The Norwegian Government created the Abel Prize for outstanding achievements in Mathematics in 2002, at the Bicentennial commemoration of the famous Norwegian mathematician Niels Henrik Abel. The Norwegian Academy has been granting it every year since 2003, and it represents the equivalent in Mathematics to the Nobel Prize awarded in other sciences. The first Abel Prize laureate was Jean-Pierre Serre. Abel Prize laureates list.
 Luis is a professor at the Univ. of Texas at Austin and was previously a professor in Minnesota, Chicago, Princeton (IAS) and New York (Courant Inst.). Luis is the first Latin-American prize-winner and the first Spanish-speaking one. He is a DHC for the Univ. Autónoma of Madrid and a foreign academician of the Royal Academy of Sciences of Spain.

* Special double issue of journal DCDS as anniversary celebration: Discrete and Continuous Dynamical Systems, Vol. 43, Nos. 3&4, March & April 2023, "Special Issue on nonlinear nonlocal diffusion equations: A 75th birthday celebration of Prof. Juan Luis Vázquez's career achievements". Eds. J. A. Carrillo (UOxford), F. d. Teso (UAM), D. Gómez-Castro (UCM). Online.

Mathematical activities and writings, 2022

* Mathematical Research in 2021-22. See list of papers and reference above, in List of Mathematical Publications 2000-2022.

* Fall workshop on nonlinear and nonlocal PDEs at Universidad Autónoma de Madrid Coorganized together with Félix del Teso, David Gómez Castro and María Medina, pdf.

Mathematical activities and writings, 2021

* Mathematical Research in 2021. See list of papers and reference above, in List of Mathematical Publications 2000-2022.

* "8th European Congress of Mathematics", held online from 20 to 26 June 2021. Main organization in Portorož, Slovenia. Coorganizer of a minisymposium with María del Mar González and Luz Roncal, pdf .

* Congress "CEDYA 2020/ CMA." Held in Gijón, Asturias, Spain in June 14-18, 2021. President of the Scientific Commitee, pdf .

* Obiturary article "En memoria de Emmanuele Di Benedetto" (1947-2021), a great mathematician and friend of the authors. By Juan José Manfredi (Pittsburgh), Miguel Ángel Herrero (UCM), and Juan Luis Vázquez (UAM). Appeared in Spanish in Boletín electrónico de la SEMA, no. 27, pp 31-38, see pdf .   Italian version here.

Life goes on. New proposals

* Concurso de ensayos Ciudad de Oviedo: “Las matemáticas de los premiados Princesa de Asturias 2020”. A mathematical Essay Contest sponsored by the Oviedo Township and organized by Real Sociedad Matemática Española, with the help of Real Academia Española de Ciencias Exactas, Físicas y Naturales and Cátedra de Inteligencia Analítica de la Universidad de Oviedo.   Announcement and bases, in Spanish.

Writings of the pandemic period

* Article "Matemáticas en los premios “Princesa” / Un regalo inesperado en el año de la pandemia: el galardón de investigación a Meyer, Daubechies, Tao y Candès." Appeared in Spanish in La Nueva España, the Oviedo newspaper, on June 28, 2020, see article in pdf. See Official announcement of Fundación Princesa de Asturias. Watch in Youtube the talk Using Math to Understand Art by Professor Ingrid Daubechies (in TEDxDuke).

* Article "Recordando a Louis Nirenberg y sus matemáticas." Appeared in La Gaceta de la Real Sociedad Matemática Española, vol. 23, June 2020, pgs. 243-261, Spanish pdf .   Extended version in English "Remembering Louis Nirenberg and his mathematics".

* Mathematical Research. See list of papers and reference in above Section List of Mathematical Publications 2000-2022.

2020 News

* 2nd IMI one-day workshop on PDEs. Fac. de Matemáticas, Univ. Complutense de Madrid, 24 Feb 2020. Speakers: R. Ferreira (UCM), L. Roncal (BCAM), J. Endal (NTNU Trondheim), X. Ros-Otón (U. Zurich), M. M. González (UAM). Organized by: F. del Teso, D. Gómez-Castro, J.L.Vázquez. Poster.

* Louis Nirenberg dies in New York (26 January 2020). A great master of Analysis in the 20th century, he received the Abel Medal along with John Nash in 2015. A quiet wise man, he was noted for the depth of his results, the elegance of his writing, and the sympathy that won him friends all over the world. My article appeared on 28 Jan 2020 in the daily newspaper La Nueva España de Oviedo. Article appeared on 31st Jan 2020 in Bulletin 653 of RSME, the Real Sociedad Española de Matemáticas, pp. 5-6, pdf.

2019 News

* Minisymposium ``Trends in nonlocal PDEs'', at ICIAM, Valencia. Title: ``Nonlinear parabolic equations driven by fractional operators''.   Coorganizer. Prof. J. I. Díaz.   Spain, July 2019.

* Stay at Imperial College of London   with a Nelder Fellowship.  Months of February and March, 2019. Proposed by Professor J. A. Carrillo.

* IMI one-day workshop on PDEs.   Organized by IMI (Univ. Complutense de Madrid).   Organizers: Jesús Ildefonso Díaz (UCM), Juan Luis Vázquez (UAM, UCM - Madrid). Dates: 18 Jan. 2019.   Poster

* ALESSIO FIGALLI, Fields medallist 2018, International Meeting.   Organized by Prof. Luigi Ambrosio   Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Pisa, Italia. Dates: 14-17 Jan. 2019.   Poster. Invited Lecture.

2018 News

* Nomination as Honorary Professor by Univ. Complutense de Madrid,
proposed by Dep. de Análisis y Matemática Aplicada de la Fac. de Ciencias Matemáticas for the academic period 2018-19, done on 1 Sept 2018. Renewed for 2019-20.

* Homenaje Multidisciplinar a los Grandes Baluartes de la UAM en su 50 Aniversario:   Aparecido como Número Extraordinario de la Revista Encuentros Multidisciplinares conmemorativo del Cincuenta aniversario de la Universidad Autónoma de Madrid. "Verdadero testimonio histórico en clave científica y multidisciplinar de la Universidad Autónoma en ese medio siglo de existencia, y ello a través de 65 muy destacados y prestigiosos protagonistas homenajeados".   Volumen.   Revista.

 ./revista.gif   Main recent research activities

* 2016-17 Warwick EPSRC Symposium: "Non-local Equations and Fractional Diffusion" Organized by José A. Carrillo (Imperial College, London), José L. Rodrigo (Univ. of Warwick), Juan Luis Vázquez (UAM - Madrid) at Univ. of Warwick, 22 - 26 May 2017.   * International Congress: "Nonlinear diffusion and free boundary problems. A conference on the occasion of the 70th anniversary of Juan Luis Vázquez". Congress poster Organized by Fernando Quirós and Matteo Bonforte, professors at Dpto de Matemáticas of Univ. Autónoma de Madrid; and held at UAM from 17 to 20 May 2017. * Scuola Estiva di Fisica Matematica Ravello 2016 XLI Summer School on Mathematical Physics, in Ravello (Italy), Sept, 12-17, 2016. Organizers: GNFM. Speakers: B. Ermentrout, A. C. Liverani, C. Negulescu, L. Preziosi, V. Romano, S. Terracini, G. Toscani, and J. L. Vázquez. * CIME Summer Course 2016 Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions in Cetraro (Italy), July, 4-8, 2016. Organizers: M. Bonforte and G. Grillo. Speakers: J. A. Carrillo, A. Figalli, R. Mingione, M. del Pino, and J. L. Vázquez. Course Lectures to appear in Springer Lecture Notes * Summer Course UIMP 2015 Frontiers of Mathematics and Applications IV in Santander (Spain), July 20-24, 2015. Main speakers: P. Daskalopoulos, S. Terracini, J. L. Vázquez, and L. Vega. * Semester Programme at the Newton Institute Free Boundary Problems in Cambridge, UK, 6 January to 4 July, 2014. Co-organizer with Henrik Shahgholian (Stockholm) and Gui-Qiang Chen (Oxford). * Summer Course UIMP 2012 Frontiers of Mathematics and Applications in Santander (Spain), August 13-17, 2012. Organizers: M. Bonforte and J. L. Vázquez. Main speakers: X. Cabré (Barcelona), L. A. Caffarelli (Texas, USA), L. C. Evans (Berkeley, USA). * Corso Estivo di Matematica Cortona 2012 Trends in Nonlinear Elliptic and Parabolic Equations Scuola Matematica Interuniversitaria held in Cortona (Italy), July 16-28, 2012. Professors: S. Terracini and J. L. Vázquez. * Workshop Centro Ennio De Giorgi Recent Trends in Nonlinear Diffusion in Pisa (Italy), 2-6 July 2012. Main organizer. * Summer School Centro Ennio De Giorgi Topics in Nonlinear Parabolic Equations in Pisa (Italy), 24-29 June 2012. Main organizer. * MSRI Semester Programme Free Boundary Problems, Theory and Applications in Berkeley, California, January to May 2011. Invited fellow. * Summer Course UIMP 2011 Frontiers of Mathematics and Applications in Santander (Spain), August 15-19, 2011. Organizers: M. Bonforte and J. L. Vázquez. * Workshop Spain-Italy Nonlinear PDEs and Functional Inequalities in Madrid (Spain) September 19-20, 2011. Organizers: M. Bonforte and J. L. Vázquez.


Institutional and personal news


Double Special Volume of the Journal Nonlinear Analysis Theory Methods & Applications, "Nonlinear Partial Differential Equations", in honor of Juan Luis Vázquez for his 70th birthday

Volume 1          Volume 2


*  Fellow of the American Mathematical Society, since 2012 AMS

*   Member of the Spanish Royal Academy of Science/ Real Academia de Ciencias Exactas, Físicas y Naturales RAC , 2013.     Discurso de Ingreso   (Acceptance address),   26 March 2014.

*  Nominated Doctor Honoris Causa by Universidad de Oviedo.   Acceptance address, 16 October 2015.

*   Nominated Fellow of the European Academy of Sciences EURASC, November 2016.

  See more professional information in Spanish in "Árbol de las Matemáticas"

imagen de ICM2006 10 years ago
ICM 2006 International Congress of Mathematicians
Held in Madrid August 22-30, 2006
The great event of the international mathematical community
organized by the International Mathematical Union (IMU)
It occurs every 4 years. First ICM: Zurich, 1897.
A famous ICM: Paris 1900. See ICM Proceedings list

My article appeared in Proceedings of ICM 2006
"Perspectives in Nonlinear Diffusion. Between Analysis, Physics and Geometry"

The slides of my Plenary Talk at ICM 2006

The curious observer

* On the scientific spirit

Galileo Galilei, one of the founding fathers of the common house of science, who was a mathematician and an experimenter at the same time, wrote in favor of clarity in science in his dialogues, like “Dialogo sopra i due massimi sistemi del mondo”. This is to be remembered in the present times where mathematics is still flooded with abstruse theories expressed in impossible language.   According to Galileo, the wise scholar must be occupied above all with being understood,  d’altro più non si cura fuorché d’essere inteso.

Aristotle, one of the great minds of Antiquity and founder of the Lyceum, recommended: before teaching something, you should know it yourself.

./math2000.gif    Blog "La República de las Matemáticas" (in Spanish)

./Alumno.gif  My Ph D studentshttp://www.telefonica.net/web2/gaiteromadrid/images/Asturies.gif

./Alumno.gif  Social occasions  Prize