Biography

A picture of myself around 1984 in the Retiro Park in Madrid, Spain.

APPOINTMENTS


EDUCATION


HONORS


HONORARY APPOINTMENTS


EDITORIAL BOARDS

Current Editorial Boards:

Past Editorial Boards:

GRANTS

I had uninterrupted grant support from the National Science Foundation of the United States during 2007-2020 as Principal or Co-Principal Investigator. I was also a member or participant of research projects in Spain and Switzerland. From 2022 to 2025 my research is supported by the BBVA Foundation, of the Spanish Bank BBVA (Banco Bilbao Vizcaya Argentaria).

  • Principal Investigator of BBVA (Banco Bilbao Vizcaya Argentaria) Foundation Grant for Scientific Research Projects with team members Sean Curry, Fraydoun Rezakhanlou and San Vu Ngoc, 2021 Call (149996 euros) 2022-2025 Spain
    (A total of 4 grants awarded for all areas of pure and applied mathematics in Spain. Details of the 2021 Call available here)
  • Co-Principal Investigator with Ioan Bejenaru and Peter Ebenfelt of National Science Foundation grant DMS-1603385 ($49080) 2016-2020 USA
  • Principal Investigator of National Science Foundation CAREER grant DMS-1518420 ($239705) 2014-2018 USA
    (Approximately 25-30 total awarded in USA per year in pure mathematics, applied mathematics and operations research, and statistics.)
  • Principal Investigator Start Up Research Grant of the University of California, San Diego ($135000) 2014-2019 USA
  • Principal Investigator of National Science Foundation CAREER grant DMS-1055897 ($386735) 2011-2014 USA
  • Co-Principal Investigator with Maciej Zworski of National Science Foundation grant DMS-0965738 ($39000) 2010-2011 USA
  • Principal Investigator of National Science Foundation Postdoctoral Fellowship DMS-0703601 ($108000) 2007-2010 USA
    (Approximately 25-30 total awarded in USA per year in pure mathematics, applied mathematics and operations research, and statistics.)
  • Member of MTM-2013-42870 of Spanish Minister of Education and Science (31921 euros) 2014-2017 Spain
  • Member of MTM-2010-21186-c02-01 of Spanish Minister of Education and Science (122600 euros) 2011-2013 Spain
  • Participant of the following grants held by Institute of Advanced Study in Princeton:
    • National Science Foundation grant DMS-1128155  (my share, $53320)  2012-2013 USA
    • National Science Foundation grant DMS-0635607 (my share, $53320) 2011-2012 USA
  • Co-Director with Nicolai Reshetikhin and San Vu Ngoc of a thematic semester in 2013, at the Bernoulli Center, where conferences were organized with a Swiss National Foundation grant ($200000) Switzerland


INVITED COLLOQUIUM AND SEMINAR TALKS

I have been invited to deliver seminar, distinguished or colloquium talks on more than 120 occasions, the following is a sample of the ones I delivered in each of these categories.

Colloquium Talks

  • Spanish Royal Academy of Sciences – Entry Speech as Corresponding Member in the Mathematical Sciences Division,  Madrid 2024 Spain. Video
  • Complutense University of Madrid 2020 Spain
  • University of Valladolid Ateneo IMUVA,  2016 Spain
  • Henri Lebesgue Center, Lebesgue Colloquium Lectures on Analysis and PDEs, 2015 France
  • ICMAT, STAMP Spectral Theory and Mathematical Physics Colloquium,  Madrid 2015 Spain
  • University of Salamanca 2015 Spain
  • University of California San Diego 2014 (twice this year) USA
  • Sydney, Sydney and UNSW Joint Colloquium, 2014 Australia
  • Spanish Royal Academy of Sciences 2014 Spain. Video
  • Humboldt University in Berlin 2014 Germany
  • University of California Berkeley 2014 USA
  • Cornell University, Oliver Club Colloquium, New York 2013 USA
  • Portland State University, Maseeh Mathematics and Statistics Colloquium,  2012 USA
  • Oxford University 2012 UK
  • Cornell University, Oliver Club Colloquium, 2012 USA
  • Washington University in St Louis 2011 USA
  • University of Texas at Austin 2011 USA
  • Washington University in St Louis 2010 USA
  • University of Rennes 2010 France
  • Yale University 2008 USA
  • Massachusetts Institute of Technology MIT, Mathematics Department January Lecture Series 2008 USA

Seminar Talks

  • Joint CRM-Montréal/Princeton/Institute for Advanced Study/Tel Aviv/Paris Symplectic Zoominar (online) 2024 USA Video
  • University of Cantabria, MATESCO Seminar 2023 Spain
  • University of Cantabria, MATESCO Seminar 2022 Spain
  • University of Granada, Geometry Day – Jornada de Geometría 2022 Spain
  • Oklahoma State University, Analysis Seminar (online) 2021 USA
  • University of Strasbourg, Analysis Seminar 2017 France
  • Complutense University of Madrid, Algebraic Geometry Seminar 2017 Spain
  • University of Rennes, Analysis Seminar 2017 France
  • Harvard University, Gauge Theory and Topology Seminar 2017 USA
  • University of Barcelona, Barcelona Analysis Seminar 2016 Spain
  • University of California Berkeley, Northern California Symplectic Seminar 2016 USA
  • University of California San Diego, Symplectic Geometry Seminar 2016 USA
  • ICMAT Madrid, Spectral Theory and Mathematical Physics Lectures 2015 Spain
  • University of Salamanca, Geometry and Topology Seminar 2015 Spain
  • Complutense University of Madrid, Geometry and Topology Seminar 2015 Spain
  • University of Zaragoza, Rubio de Francia Memorial Seminar 2015 Spain
  • University of California Los Angeles, Analysis and PDE Seminar 2015 USA
  • University of California Irvine, Geometry and Topology Seminar 2015 USA
  • Cornell University, Topology Seminar 2014 USA
  • Complutense University of Madrid, Geometry and Topology Seminar 2014 Spain
  • University of Melbourne, Statistical Mechanics Seminar 2014 Australia
  • University of Illinois Urbana-Champaign, Symplectic and Poisson Geometry Seminar 2013 USA
  • University of Texas at Austin, Analysis Seminar 2013 USA
  • Stanford University, Northern California Symplectic Geometry Seminar 2013 USA
  • Princeton University and Institute for Advanced Study Joint Symplectic Seminar 2013 USA. Video
  • ICMAT Madrid, Geometry Seminar 2013 Spain
  • Penn State University, Geometry Seminar 2012 USA
  • Brandeis University, Topology Seminar 2011 USA
  • University of Chicago, Geometry and Topology Seminar 2011 USA
  • University of Wisconsin Madison, Geometry and Topology Seminar 2011 USA
  • Washington University in St Louis, Geometry Seminar 2011 USA
  • Cornell and Penn State Joint Symplectic Seminar 2011 USA
  • Institute for Advanced Study in Princeton, Members Seminar 2011 USA. Video
  • Institute for Advanced Study in Princeton, Introductory Lectures by New Members 2011 USA. Video
  • Institute for Advanced Study in Princeton, Mathematical Conversations 2011 USA. Video
  • University of Texas at Austin, Analysis Seminar 2011 USA
  • University of Washington Seattle, Geometry and Combinatorics Seminar 2010 USA
  • University of California Berkeley, Symplectic Geometry Seminar 2010 USA
  • University of Paris-XI, Orsay, Topology and Dynamics Seminar 2010 France
  • Complutense University of Madrid, Geometry and Topology Seminar 2010 Spain
  • Johns Hopkins University, Topology Seminar 2009 USA
  • University of Washington Seattle, Geometry and Combinatorics Seminar 2008 USA
  • University of Washington Seattle, Pre-Combinatorics Seminar 2008 USA
  • Brandeis University, Every-Topic/Every-Person Seminar 2008 USA
  • Massachusetts Institute of Technology MIT, Group Actions in Geometry Seminar 2008 USA
  • Massachusetts Institute of Technology MIT, PDE and Analysis Seminar 2007 USA
  • Brown University, Geometry and Topology Seminar 2007 USA
  • Stanford University, Northern California Symplectic Geometry Seminar 2007 USA
  • CRM University of Quebec in Montreal, Symplectic Topology Seminar 2007 Canada
  • Harvard University, Gauge Theory and Topology Seminar 2007 USA
  • Swiss Federal Institute of Technology in Lausanne, Geometric Analysis Seminar 2007 Switzerland
  • Fourier Institute, Grenoble, Joint Mathematical Physics and Topology Seminar 2007 France
  • University of Washington Seattle, Geometry and Combinatorics Seminar 2007 USA
  • University of Washington Seattle,  Pre-Combinatorics Seminar 2007 USA
  • Boston University, Geometry Seminar 2007 USA
  • Brandeis University, Topology Seminar 2007 USA
  • University of Toronto, Symplectic Geometry Seminar 2007 Canada
  • University of Chicago, Geometry/Topology Seminar 2006 USA
  • Boston University, Geometry Seminar 2006 USA
  • Massachusetts Institute of Technology MIT, Geometry Seminar 2006 USA
  • Stony Brook University, Geometry Seminar 2006 USA
  • Ohio State University, Topology Seminar 2006 USA
  • University of Michigan, Topology Seminar 2005 USA
  • University of Michigan, Geometry Seminar 2005 USA
  • University of Toronto, Symplectic Geometry Seminar 2004 USA
  • Michigan State University, Symplectic Geometry Seminar 2004 USA
  • University of Michigan, Topology Seminar 2004 USA


INVITED CONFERENCE AND CONGRESS TALKS

I have received over 60 invitations to deliver talks at congresses and international conferences, of which I have delivered approximately half of them (among the ones I didn’t accept because of calendar problems are plenary congress talks in the Poisson 2012 Conference and the Joint Congress of the Royal Spanish Mathematical Society with the Belgium and Luxembourg mathematical societies). The following is a sample of the talks I delivered.

  • BBVA Foundation Project Opening Lecture at Conference Symplectic and Algebraic Geometry of real and p-adic systems, Complutense University of Madrid, June 10,11 and 12 of 2024
  • Lecture at Congress deLeonfest 2023, An Interdisciplinary Conference on Geometric Mechanics and Related Fields, in honor of Manuel de León in Madrid, December 11-13, 2023 Spain
  • BBVA Foundation Project Opening Lecture at Conference Stability, Quantization and Randomness in Symplectic Geometry – Dedicated to Professor Pedro Luis García Pérez on his 85th birthday, Complutense University of Madrid, June 28, 2023 Spain. Video
  • Plenary at VII Iberoamerican Meeting on Geometry, Mechanics and Control (online) in Bahía Blanca, March 7-11, 2022 Argentina
  • Plenary at Symposium New Developments in Momentum Polytope Theory at ICMAT (online),  July 26-30, 2021 Spain; and two Minicourse Lectures in Summer School on the same topic (online), August 2-5, 2021 Spain
  • Plenary at Congress Geometric Properties of Momentum Maps and Integrability in Ascona, April 4-7, 2018 Switzerland
  • Plenary at Congress Integrable Systems in Ascona, 19 June-24 June 2016 Switzerland
  • Plenary at Congress Symplectic Techniques in Topology and Dynamics 2015 in Cologne, August 24-28, 2015 Germany
  • Plenary at Congress Geometric Analysis in honor de Tudor Ratiu on his 65th birthday,  June 12-13, 2015, Ecole Polytechnique Federale de Lausanne, Switzerland
  • Plenary at Southern California Analysis and PDE Conference May 2-3, 2015 USA
  • Plenary at Congress Poisson Geometry in Mathematics and Physics in Urbana, August 4-8, 2014 USA. Video
  • Invited at Special Session of the First Joint international Meeting RSME-SCM-EMA-SIMAI-UMI in Bilbao, July 4, 2014 Spain
  • Plenary at Congress De León Fest in honor of Manuel de León in Madrid, December 16-19, 2013 Spain
  • Plenary at Congress Finite Dimensional Integrable Systems in Marseille, 15-19 July 2013, France
  • Plenary at Congress in honor of Alan Weinstein in the Bernoulli Center in Lausanne, July 22-26, 2013 Switzerland
  • Plenary at the 20th International Workshop on Geometry and Physics, Madrid, August 31-September 3, 2011 Spain
  • Plenary at Congress of Jóvenes Investigadores de la RSME, Soria 2011 Spain
  • Invited at the American Mathematical Society 2011 Spring Southeastern Section Meeting 2011 USA
  • Plenary at the Centennial Congress of the Royal Spanish Mathematical Society, Avila, 2011 Spain
  • Plenary at the Congress Mechanics, Geometry and Dynamics, en honor de Tudor Ratiu on his 60th birthday, July 12-16, 2010, CIRM Luminy, France
  • Invited at the Special Session Invariants of Lie Group Actions and Their Quotients of the American Mathematical Society 2007 Fall Eastern Section Meeting 2007 USA
  • Invited at the Special Session on Toric Varieties of the American Mathematical Society 2007 Fall Eastern Section Meeting 2007 USA
  • Invited at the Special Session on Low Dimensional Topology and Geometry, IV of the American Mathematical Society 2006 Fall Western Section Meeting 2006 USA
  • Invited at the Special Session on Combinatorial Methods in Equivariant Topology of the American Mathematical Society 2006 Fall Eastern Section Meeting 2006 USA
  • Invited at Congress Transformation Groups in Geometry and Topology in Amherst 2008 USA
  • Invited at Congress Sixth Conference on Geometry and Physics CRM en Barcelona 2008 Spain
  • Invited at Congress Lie Groups in Analysis and Mechanics en Utrecht 2004 The Netherlands


SCIENTIFIC COMMITTEES AND ORGANIZATION

I have served on the scientific committees for a number of conferences in Europe and the United States, and have been program director of many scientific events. Most recently I was on the speaker selection committee for the Eight Pacific Rim Conference 2020 in Berkeley, and the Finite Dimensional Integrable Systems in Geometry and Mathematical Physics 2019 and 2023 conferences (one of the the main regular conferences in finite dimensional integrable systems). The following is a selection of other scientific events which I have organized or co-organized.

  • BBVA Foundation Project Conference: Symplectic and Algebraic Geometry of Real and p-adic Systems, Complutense University of Madrid, June 10,11 and 12 of 2024.
  • BBVA Foundation Project Conference: Combinatorial Problems in Algebraic and Symplectic Geometry, Complutense University of Madrid, November 8 of 2023, Spain.
  • BBVA Foundation Project Conference: Stability, Quantization and Randomness in Symplectic Geometry – Dedicated to Professor Pedro Luis García Pérez on his 85th birthday, Complutense University of Madrid, June 28-30, 2023, Spain
  • Southern California Analysis and PDE Conference at the University of California San Diego California, November 2-3, 2019, USA
  • Southern California Analysis and PDE Conference at the University of California San Diego California, April 1-2, 2017, USA
  • Symplectic Geometry Seminar at the University of California San Diego, Winter, Spring 2016, Winter 2017, Winter 2018 USA
  • 9th ICMAT International Geometry, Mechanics and Control Summer School on Symplectic Geometry, Classical Mechanics, and Interactions with Spectral Theory at Residencia La Cristalera, Madrid,  June 29-July 3, 2015 Spain
  • Geometry, Mechanics and Control Seminar at the University of California San Diego, Winter 2015 USA
  • Conference Geometry and Semiclassical Analysis in Interaction with Spectral Theory and Physics at ICMAT Madrid, June 9-13, 2014, Spain
  • Congress Beyond Toric Integrability at the Bernoulli Center of Lausanne, December 9-13, 2013, Switzerland
  • Special Session on Spectral, Index, and Symplectic Geometry at the Fall Central Sectional Meeting of the American Mathematical Society, October 18-20, 2013 in Saint Louis USA
  • Congress in Honor of Alan Weinstein at the Bernoulli Center in Lausanne, July 22-26, 2013, Switzerland
  • Congress Integrable Systems and Semiclassical Analysis at the Bernoulli Center in Lausanne, July 8-12, 2013, Switzerland
  • Summer School Integrable Systems and Semiclassical Analysis (Bernoulli Center in Lausanne) July 1-5, 2013 Switzerland
  • Special Session on Symplectic and Poisson Geometry at the Spring Southeastern Section Meeting of the American Mathematical Society in Georgia, March 12-13, 2011, USA
  • Joint IAS-Princeton Symplectic Geometry Seminar 2011-2012 USA
  • Geometry Seminar at the Institute for Advanced Study in Princeton 2011-2012 USA
  • Congress Symplectic and Poisson Geometry in interaction with Algebra, Analysis and Topology, May 4-7, 2010 at MSRI Berkeley California, USA


OTHER PROFESSIONAL ACTIVITIES

As part of my normal duties I have served on numerous university committees at the different universities where I have been. Beyond these duties I have had many responsibilities on international boards and executive committees in a number of capacities, as well as been a panelist for top level grant programs by leading research agencies such as the National Science Foundation in the United States and the BBVA Foundation in Spain, including several regarded as the most competitive grants like:

Furthermore, I have been evaluator of some of the most competitive international fellowships for scientists who are in the early stages of their career as well as top awards for collaborative research including:

I was also on the speaker selection committee for the International Congress on Mathematical Physics (which in 2021 took place in Switzerland), the most important congress in mathematical physics worldwide, and which is celebrated every three years.

In addition, I was a member of the Spanish Royal Mathematical Society Committee on International Affairs and represented the society before the American Mathematical Society for many years. In Spain I was twice a member of the Rubio de Francia Prize Committee, (2013 edition and 2014 edition)  which is the most important prize awarded by the Royal Spanish Mathematical Society.

While I was a member of the Institute for Advanced Study in Princeton I represented the School of Mathematics of the Institute at one of the yearly Board of Trustees Meetings.


SUMMARY OF PUBLISHED RESEARCH

I have written about sixty research papers primarily in the area of differential geometry, with an emphasis on symplectic geometry (I wrote this general audience introduction to symplectic geometry, for the BBVA Foundation, in Spanish). Some of these works have an interdisciplinary component in that they have a substantial intersection with at least another area of mathematics (notably integrable systems, spectral theory, homotopy type theory and probability). The journal in which I have published the most papers is Communications in Mathematical physics (2006, 2012, 2014, 2024), which represents well my interest in mathematical problems with a substantial connection to physics. I have published papers in top mathematics journals such as Acta Mathematica and Inventiones Mathematicae as well as in some of the leading specialized journals in differential geometry. The complete list of my published works is available in the section of Publications, and a few highlights about these works are available in the section of Research.


RESEARCH EVALUATIONS

My entrance score for the Spanish category of Catedrático de Universidad (Full Professor) was 99.4 out of 100. This score represents a number between 1 and 100 assigned to candidates competing for university positions in open competition (Concurso-Oposición).

In 2021 I was awarded by the Spanish Ministry of Universities National Agency for Quality Assessment and Accreditation ANECA three positive and consecutive six-year research periods (called “sexenios de investigacion”) for years 2002-2007, 2008-2013, and 2014-2019.


PERSONAL

I was born in Madrid, Spain, in 1978. According to the university public data available in the Portal de Transparencia, in the year 2020 there were precisely 3 Catedráticos de Universidad (Full Professors) who were 44 years old or younger, on the faculty at the Complutense University of Madrid, out of a total of 782 (of a total of 6251 faculty members). Of these, 122 were under the age of 55.

Education is the best provision for the journey to old age.
Aristotle