Research and Projects

Research Topics:

• Kinetic equations: asymptotic behavior, modelling
  and numerical simulation.
• Nonlinear diffusion equations: asymptotic behavior
  and qualitative properties.
• Applications of kinetic equations: charged particles
  transport in semiconductors and plasmas, rarefied gas dynamics, granular
  gases…
• Kinetic and Diffusive Models in Mathematical Biology: chemotaxis, swarming and flocking, computational neuroscience…
• Numerical methods for nonlinear conservation laws.

I was honoured to be included in the Siam Fellow Class 2019.

You can listen to my Inaugural Lecture at Imperial College to understand part of my research.

Some recent talk at Simon Fraser University on Repulsive-Attractive models.

An interview about the 2018 Year of Mathematical Biology.

An article in El Pais about computational neuroscience.

A wide audience talk during the Spanish National Day celebration online at the Spanish Embassy in London on 2020 (1h:06m).

A wide audience talk at The Queen´s College Symposium.

You can also listen to the 3-minute Thesis competition at Imperial College by my PhD student Franca Hoffmann.

I won the 2016 SACA award for best supervisor nominated by my own PhD students!!

An interesting discussion with diplomats of the Spanish Embassy in London.

My Proust Test for the SIMAI.

Projects:

• ERC Advanced Grant 2019: Nonlocal-CPD (Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization)
  of the European Research Council Executive Agency (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 883363), October 2020 – October 2025.
• EPSRC Grant: Nonlinear Nonlocal
  Aggregation-Diffusion Partial Differential Equations and
  Applications, March 2013 – March 2016.
• EPSRC Grant: Nonlocal Partial Differential Equations: entropies, gradient flows, phase transitions and applications,
  September 2017 – March 2021. Principal Investigator: Greg Pavliotis,
  Co-I: José A. Carrillo.
• EPSRC Grant:
  Spectral element methods for
  fractional differential equations, with applications in applied
  analysis and medical imaging, July 2021 – July 2024. Principal Investigator:
  Sheehan Olver, Co-I: José A. Carrillo.
• Royal Society Wolfson Research Merit Award, October 2012 – September 2017.
• International Exchanges Scheme of the Royal Society-CNRS, March 2014 – June 2016.
• International Exchanges Scheme of the Royal Society-Japan, August 2015 – August 2017.
• International Exchanges Scheme of the Royal Society-HongKong, May 2017.
• KI-net,
  Kinetic description of emerging challenges in multiscale problems of natural sciences,
  NSF Research Network in Mathematical Sciences, 2012-2016. Node: University of Cambridge.
• Proyecto MICINN MTM2011-27739-C04-02/MTM: Ecuaciones en derivadas parciales en
  Física y Biología-Matemática: modelos micro y macroscópicas. Principal Investigator till October 2012. January 2012-December 2015.
• Proyecto MTM2014-52056-P: EDPs no locales para sistemas de partículas: análisis y simulación numérica. Principal Investigator: José A. Cañizo. Participating Foreign Investigator. January 2015-December 2017.

Editorial Board Member:

• Editorial Board of Kinetic
  and Related Models, 2008–.
• Editorial Board of Publicacions Matemàtiques, 2009–.
• Editorial Board of Rivista Matematica della Università di Parma, 2010–.
• Editorial Board of SIAM Journal on Mathematical Analysis (SIMA), 2010–.
• Editorial Board of
  AIMS Book Series in Applied Mathematics, 2011–.
• Editorial Board of
  Discrete and Continuous Dynamical Systems – Series A (DCDS-A), 2013–.
• Editorial Board of Journal of the London Mathematical Society, 2013–.
• Editorial Board of Bulletin of the London Mathematical Society, 2013–.
• Editorial Board of
  Interfaces and Free Boundaries: Mathematical Analysis, Computation and Applications, 2014–.
• Editorial Board of Journal of Elliptic and Parabolic Equations, 2014–.
• Editorial Board of Advances in Differential Equations, 2015–.
• Editorial Board of
  Communications in Contemporary Mathematics, 2016–.
• Editorial Board of
  SeMA Journal, 2016–.
• Editorial Board of
  Royal Society Open Science, 2016–.
• Editorial Board of Transactions of Mathematics and its Applications: A Journal of the IMA, 2017–.
• Editorial Board of Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2017–.
• Editorial Board of
  De Gruyter Series in Applied and Numerical Mathematics, 2017–.
• Editorial Board of
  Quarterly of Applied Mathematics, 2018–.
• Editorial Board of
  Boletín de la Sociedad Matemática Mexicana, 2018–.
• Editorial Board of
  Advances in Nonlinear Analysis, 2021–2025.
• Editorial Board of Networks
  & Heterogeneous Media, 2021–.

Past Editorial Boards:

• Editorial Board of Mathematics, 2013-2014.
• Editorial Board of Proceedings of the London Mathematical Society, 2013–2019.
• Editorial Board of Nonlinear Analysis and Differential Equations, 2015–2020.
• Editorial Advisory Board of Open Mathematics, 2018–2019.
• Editorial Board of Acta Applicandae Mathematicae, 2010–2020.

Awards and Recognition:

• SeMA Young Researcher Prize 2003.
• Richard von Mises Prize of the International Association of Applied Mathematics and Mechanics (GAMM) 2006.
• Royal Society Wolfson Research Merit Award 2012.
• 2016 SACA award for best supervisor.
• Member of the European Academy of Sciences 2018-.
• Changjiang Visiting Scholar, Ministry of Education of China, 2018-2021.
• Siam Fellow Class 2019.
• 2026 Class of Fellows of the AMS.
• 1st cohort of Fellows of the UK Academy of the Mathematical Sciences.

Committee Members:

• Vicepresident of the European Society for
  Mathematical and Theoretical Biology, 2021-2023.
• Head of the Division of Mathematics of the European Academy of
  Sciences 2020-2022.
• Program Officer of the SIAG in Analysis of PDEs 2019-2020.
• Chair of the
  Year of Mathematical Biology 2018.
• Chair of the
  Applied Mathematics Committee of the European Mathematical Society, 2014-2017.
• Member of the
  Applied Mathematics Committee of the European Mathematical Society, 2010-2013.
• Member of the ECMI Council, 2005- October 2012.

Science Policy:

• Member of the Science Policy Committee of the SRUK/CERU.
• Informe de Recomendaciones sobre la I+D en España para las Elecciones Generales SRUK.
• Taller: CienciaUK 2015. La carrera investigadora y alternativas profesionales en Reino Unido. Fundación Ramón Areces, Madrid 27 de Noviembre de 2015.

Research News:

• Sergio Pérez: UROP Student Departamental Award 2015.
• Franca Hoffmann: Imperial College Student Award for Outstanding Achievements 2017.
• Sergio Pérez: Imperial College Student Award for Outstanding Achievements 2019.