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Advanced Courses
Lectures on
PDEs and Geometry

UAM Madrid (Spain)
February 5-7, 2018
Course by Felix Otto
Parabolic equations with rough coefficients and singular forcing.
Next, March 12-16, 2018
Course by Susanna Terracini

Past Events

Nonlinear diffusion and free boundary problems. A conference on the occasion of the 70th anniversary of Juan Luis Vázquez
UAM Madrid (Spain)
May 17-19, 2017

Summer Course
CIME 2016
Nonlocal and nonlinear diffusions and interactions
New methods and directions

Cetraro (Italy)
July 4-8, 2016

Summer Course
Frontiers of Mathematics and Applications IV
Santander (Spain)
July 20-24, 2015

Postal Address...

Departamento de Matemáticas
Universidad Autónoma de Madrid
Campus de Cantoblanco
28049 Madrid

...and more

Building 17 (ex C-XV), Office 405

    [phone]             (+34) 91 497 69 32
[fax]    (+34) 91 497 48 89

Actual Position

I am a Professor (Contratado Doctor, I3) of the Departamento de Matemáticas at the Universidad Autónoma de Madrid.

I am PI2 of the Spanish research group MTM2014-52240-P, "Ecuaciones de Difusión No Lineales y Aplicaciones" - "Nonlinear Diffusion Equations and Applications" - PI1 Juan Luis Vázquez and founded by MINECO (Spanish Government).

I am member of the editorial board of the Journal Nonlinear Analysis.

In this academic year 2017/2018 I am teaching two courses at UAM: Advanced Course in Partial Differential Equations for students of the Master in Mathematics and Mathematical Modeling for students of the 3rd-4th year of Mathematics.

Research Interests

Nonlinear and/or nonlocal partial differential equations:
asymptotic properties, rates of convergence to equilibrium, regularity and Harnack inequalities for degenerate and singular nonlinear -and also nonlocal- parabolic PDE in the Euclidean setting and on Riemannian manifolds. Nonlinear (fast) diffusion flows of porous medium or p-Laplacian type. Total variation flow.

Functional inequalities (also with weights): Sobolev, Gagliardo-Nirenberg, Hardy, Poincaré, Logarithmic Sobolev, [...] and their application to PDE.

Entropy methods for nonlinear flows, in the Euclidean setting and on Riemannian manifolds: a bridge from functional inequalities to PDE and geometry.