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BIRS-IMAG Workshop
Nonlinear Diffusion and nonlocal Interaction Models - Entropies, Complexity, and Multi-Scale Structures (23w6003)

IMAG Granada (ES)
May 28 June 2, 2023

2023 Thematic Period on PDES
Diffusion, Geometry,
Probability and Free Boundaries

June-December 2023

Past Events

BIRS-CMO Workshop
New Trends
in Nonlinear Diffusion:
a Bridge between PDEs,
Analysis and Geometry
(Online) (21w5127)

CMO Oaxaca (online)
September 6-10, 2021

2020 Fields Medal Symposium
Alessio Figalli

Online Event
Fields Institute, Toronto
October 19 - 23, 2020

Workshop in honor of Alessio Figalli’s Doctor Honoris Causa at UPC. Five talks and a Round Table with Prof. A. Figalli.
Universitat Poltitecnica de Catalunya, Barcelona, ES, November 21, 2019

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 Titular of the Departamento de Matemáticas at the Universidad Autónoma de Madrid.

I am co-PI with Mar Gonzalez of the Spanish research group MTM2017-85757-P, " EDPs No-Lineales: Difusión, Geometría y Aplicaciones" - "Nonlinear PDEs: Diffusion, Geometry and Applications", founded by MINECO (Spanish Government).

I am a Faculty member of ICMAT Instituto de Ciencias Matemáticas

I am co-organizing the 2023 Thematic Period on PDEs Diffusion, Geometry, Probability and Free Boundaries at UAM-ICMAT Madrid (ES) in the period June-December 2023.

I am member of the editorial board of the Journal Nonlinear Analysis: Real World Applications.

Research Interests

Nonlinear and/or nonlocal partial differential equations:
asymptotic properties, rates of convergence to equilibrium, Harnack inequalities, higher and boundary regularity for degenerate and singular nonlinear -and also nonlocal- parabolic (and elliptic) 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, Caffarelli-Kohn-Nirenberg [...] and their application to PDE. Quantitative and constructive stability properties for Gagliardo-Nirenberg-Sobolev inequalities

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