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 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.
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
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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
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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"
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.
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