Nigel Hitchin and Ngô Bảo Châu Laboratory

Chairmen

Nigel Hitchin (University of Oxford)

Nigel Hitchin is Emeritus Savilian Professor of Geometry at the University of Oxford, UK. He received a D.Phil. in Mathematics at the University of Oxford in 1972, under the supervision of Sir Michael Atiyah, and carried postdoctoral research at the Institute for Advanced Study in Princeton in 1971–1973. After a year at the Courant Institute, he returned to Oxford, where he had several appointments at Wolfson College (1974–1979) and St Catherine’s College (1979-90). He was Professor of Mathematics at the University of Warwick (1990–1994), and the Rouse Ball Professor of Mathematics at the University of Cambridge (1994–1997). In 1997, Nigel Hitchin returned to Oxford, as the Savilian Professor of Geometry and a Professorial Fellow at New College, chair that he occupied for 20 years.

His main scientific contributions fall in the fields of differential geometry, algebraic geometry and mathematical physics. His discoveries at the interface of pure mathematics and physics have opened new areas of research in a substantial number of fields, including spin geometry, instanton and monopole equations, twistor theory, symplectic geometry of moduli spaces, integrables systems, Higgs bundles, Einstein metrics, hyperkähler geometry, Frobenius manifolds, Painlevé equations, special Lagrangian geometry and mirror symmetry, and generalized geometry. These contributions have found wide applications, among others in the geometric Langlands programme, string theory and supergravity.

Nigel Hitchin has had many visiting appointments, including the Institut des Hautes Études Scientifiques (1975, 1979, 1987, 1990, 1994, 1997), École Normale Superieure Paris (1979), the University of Bonn (1979), the Institute for Advanced Study in Princeton (1982), SUNY Stony Brook (1983–1984), ÃLcole Polytechnique (1988), Universidad Autónoma de Madrid (2001), Simons Center for Geometry and Physics, Stony Brook (2011), and ICMAT, Madrid (2013–2019). He has been the President of the London Mathematical Society (1994–1996), and served as a member of numerous national and international committees, including the Program Committee for ECM2008 and the Fields Medal Committee for ICM2018. He is frequently called upon to give named lectures in the USA, Canada, China and Europe.

Professor Hitchin is a member of the editorial board of the Journal of Differential Geometry, International Mathematics Research Notices, and Annals of Global Analysis and Geometry, having served in the past in the editorial board of many other journals, like Mathematische Annalen, Topology, Journal of Topology, etc. He is also in the editorial board of the Springer book series Grundlehren der mathematischen Wissenschaften, and Oxford University Press Mathematical Monographs.

Among his many distinctions, he has won the Shaw Prize in Mathematical Sciences (2016), the Whitehead (1980) Berwick (1990) and Polya (2002) prizes of the London Mathematical Society, and the Sylvester Medal of the Royal Society (2000). He is a Fellow of the Royal Society (elected in 1991), an Honorary Fellow of Jesus College (elected in 1998), and a fellow of the American Mathematical Society (elected in 2012). He was awarded an Honorary Degree (Doctor of Science) from the Universities of Bath (2003) and Warwick (2014).

Ngô Bảo Châu (University of Chicago)

Ngô Bảo Châu is Professor of Mathematics at the University of Chicago, USA. He received his PhD in Mathematics in 1997 at the Université de Paris Sud under the supervision of Gérard Laumon. After that he was a CNRS Fellow at Université de Paris Nord (1998–2004), Professor at the Université de Paris Sud (2004–2007), and Long-term Member of the Institute for Advanced Study at Princeton (2007–2010), moving to the University of Chicago in 2010. He also holds currently a Visiting Chair at the Collège de France (Paris) for 2020–2025, and is Scientific Director of the Vietnam Institute for Advanced Study in Mathematics since 2011.

His main mathematical contributions fall in the fields of algebraic geometry, number theory and geometric representation theory. He is best known for his proof of the “Fundamental Lemma” of the Langlands Programme, for which he was awarded a Fields Medal in 2010. In his proof he uses in an essential way the Hitchin fibration of the moduli space of Higgs bundles introduced by Hitchin in 1987. His proof of the Fundamental Lemma ranked seventh on Time magazine’s Top 10 Scientific Discoveries of 2009 list[1]. Ngô’s proof has opened the door to many further advances, in particular, in the general theory of automorphic representations and Shimura varieties. Independently of its applications, the peculiar challenge of the Fundamental Lemma has spurred many ingenious advances of standalone interest. His proof spans many areas, appealing to remarkable new ideas in representation theory, model theory, algebraic geometry, and algebraic topology.

Professor Ngô has delivered named lectures in the USA, Canada, Europe, Japan and Singapore, as well as a sectional talk in the ICM2006 in Madrid and a plenary talk in the ICM2010 in Hyderabad. He is in the editorial board of Nagoya Mathematical Journal, Compositio Mathematica, Acta Mathematica Vietnamica, Vietnam Journal of Mathematics and the Springer book series Grundlehren der mathematischen Wissenschaften, having served in the past in the editorial board of Inventiones Mathematicae and Mathematisch Zeitschrift.

In addition to obtaining a Fields Medal in 2010 and ranking 7th in the Time magazine Top 10 Scientific Discoveries of 2009, as mentioned above, Professor Ngô has had many distinctions and recognitions, including a Clay Research Award (2004), the Sophie Germain Prize given by the Académie des Sciences de Paris (2007), the Oberwolfach Prize (2007), the Légion d’honneur (2011), and an Honorary Doctoral Degree by the Vietnam National University (2011). He is a Fellow of the American Mathematical Society (2012), a Member of the American Academy of Arts and Sciences (2012), and a Foreign Member of the Académie des Sciences de Paris (2016).

ICMAT coordinator

Oscar García-Prada (ICMAT-CSIC)

Oscar García-Prada is a CSIC Research Professor at Instituto de Ciencias Matemáticas (ICMAT, Madrid). He obtained a D.Phil. in Mathematics at the University of Oxford in 1991 under the supervision of Nigel Hitchin and Simon Donaldson, and had postdoctoral appointments at Institut des Hautes Études Scientific (Paris), University of California at Berkeley, and University of Paris-Sud, before holding positions at University Autónoma of Madrid and École Polytéchnique (Paris). In 2002 he joined the Spanish National Research Council (CSIC).

His research interests lie in the interplay of differential and algebraic geometry with differential equations of theoretical physics, more concretely, in the study of moduli spaces of Higgs bundles, character varieties of surface groups and higher Teichmüller spaces, as well as gauge-theoretic equations and related equations emerging from infinite dimensional moment maps. Professor García-Prada serves as editor in several international journals, including the International Journal of Mathematics and the Illinois Journal of Mathematics, having served in the past in the editorial board of Geometriae Dedicata. He participates regularly in public outreach activities on mathematics and their interactions with physics and music, collaborating with the newspapers El País and El Mundo, Spanish Radio Exterior, Spanish television RTVE and the Residencia de Estudiantes in Madrid.

Faculty

Luis Álvarez Cónsul (ICMAT)
José Ignacio Burgos Gil (ICMAT)
Mario García Fernández (ICMAT)
Emilio Franco (ICMAT-UAM)
Oscar García Prada (ICMAT), Coordinator
Tomás Gómez de Quiroga (ICMAT)

- External collaborators:
- Nigel Hitchin (University of Oxford), Chair
- Ngô Bảo Châu (University of Chicago), Chair
- Kevin Corlette (University of Chicago)
- Victor Ginzburg (University of Chicago)
- Xenia de la Ossa (University of Oxford)

Postdoctoral researchers

Mathieu Ballandras (ICMAT-CSIC)
King Leung Lee (ICMAT-CSIC)
Alberto Navarro (ICMAT-CSIC)
Arpan Saha (ICMAT-CSIC)
- External collaborators:
- Iván Blanco-Chacón (Universidad de Alcalá de Henares)
- Benedict Morrisey (University of Chicago)

PhD students

Jesús Aguado López (ICMAT-UCM)
Andoni de Arriba de la Hera (ICMAT-UCM)
Guillermo Barajas Ayuso (ICMAT-UAM)
Bilson Castro (ICMAT-UAM)
Guillermo Gallego Sánchez (ICMAT-UCM)
Raúl González Molina (ICMAT-UAM)
Roberto Téllez Domínguez (ICMAT-UAM)
Enrique Martínez (ICMAT-UAM)

- External collaborators:
- Mateo Galdeano Solans (University of Oxford)
- Thomas Hameister (University of Chicago)
- Enrico Marchetto (University of Oxford)
- Griffin Wang (University of Chicago)

Associate members