Christophe Breuil

Christophe Breuil is a French mathematician noted for contributions to number theory, particularly the modularity of Galois representations and the theory of modular forms. He played a central role in collaborative work that advanced the proof of the modularity theorem for elliptic curves and in developments connecting p-adic Hodge theory, representation theory, and arithmetic geometry. Breuil has held positions at prominent French institutions and has been recognized by major mathematical organizations.

Early life and education

Breuil was born in France and completed his higher education at institutions including Université Paris-Sud where he obtained advanced degrees. He pursued doctoral studies under advisors associated with research groups at places such as Institut des Hautes Études Scientifiques, Centre National de la Recherche Scientifique, and laboratories connected to Université Paris-Sud. During his formative years he interacted with mathematicians from institutions like École Normale Supérieure, Université Pierre et Marie Curie, Université Paris Diderot, Collège de France, and international centers including Harvard University and University of Cambridge.

Academic career and positions

Breuil has held faculty and research positions at French and international institutions including École Normale Supérieure, Collège de France, École Polytechnique, and research roles within Centre National de la Recherche Scientifique. He has been affiliated with research institutes such as Institut des Hautes Études Scientifiques and has collaborated with mathematicians at Princeton University, Massachusetts Institute of Technology, University of Chicago, University of California, Berkeley, Stanford University, University of Oxford, University of Cambridge, Imperial College London, Max Planck Institute for Mathematics, RIKEN, and Kavli Institute for the Physics and Mathematics of the Universe. Breuil has supervised doctoral students who later took positions at universities like Université Paris-Sud, Université Paris-Saclay, Université de Strasbourg, Université Grenoble Alpes, University of Warwick, University of Bonn, École Polytechnique Fédérale de Lausanne, and University of Zurich.

Research contributions and results

Breuil's research has concentrated on the interaction of modular forms, Galois representations, and p-adic methods. He contributed to the proof of modularity results related to the Taniyama–Shimura conjecture, now often called the Modularity theorem, working in contexts connected to the breakthroughs of Andrew Wiles, Richard Taylor, Christopher Skinner, and Barnet-Lamb, Geraghty, Harris, Taylor-style developments. His work on p-adic Hodge theory intersects with foundational results by Jean-Marc Fontaine, Pierre Colmez, Kazuya Kato, and Luc Illusie. Breuil developed structures now known as Breuil modules, which interface with theories of Fontaine–Laffaille theory, (phi,Gamma)-modules, and the classification of semi-stable representations, building on insights from Jean-Pierre Serre, Jean-Louis Verdier, Serre-related conjectures, and the Langlands program. He collaborated with researchers like Brian Conrad, Fred Diamond, Richard Taylor, Peter Sarnak, Mark Kisin, Toby Gee, David Geraghty, Michael Harris, Gerard Laumon, Lucien Szpiro, and Gabriel Dospinescu on themes linking modular curves, Shimura varieties, Hecke algebras, and the arithmetic of elliptic curves.

Breuil's contributions to p-adic representation theory informed the work on p-adic local Langlands correspondences for GL2(Q_p), connecting with results by Colmez, Emerton, Breuil–Mézard conjecture collaborators such as Mark Kisin and M. Emerton-related developments. His research influenced advances in the study of deformation rings, the weight part of Serre's conjecture, and the modularity lifting techniques used in the work of Calegari, Geraghty, Khare, and Wintenberger.

Awards and honors

Breuil has received recognition including the Clay Research Award and invitations to speak at major venues like the International Congress of Mathematicians. His work has been acknowledged by institutions such as the Académie des sciences (France), Société Mathématique de France, and award committees linked to organizations like the European Mathematical Society and International Mathematical Union. He has held visiting appointments and fellowships at centers including the Institute for Advanced Study, Mathematical Sciences Research Institute, and IHÉS.

Selected publications

- Breuil, Christophe; Collaborators. Papers on p-adic representations, modularity, and Breuil modules in journals associated with Annals of Mathematics, Inventiones Mathematicae, Duke Mathematical Journal, Journal of the American Mathematical Society, and proceedings of conferences organized by Bernard Dwork, Alexander Grothendieck-related schools. - Breuil, Christophe. Works on the p-adic local Langlands correspondence for GL2(Q_p) with follow-up articles in venues linked to Pierre Deligne, Jean-Pierre Serre, and Alexander Grothendieck-themed volumes. - Breuil, Christophe; Emerton, Matthew; Collaborations on modularity lifting and p-adic representations appearing in collections associated with Cornell University and publishers like Springer and American Mathematical Society.

Category:French mathematicians Category:Number theorists