Ngo Bao Chau

Ngo Bao Chau
Nguyentrongphu · CC BY-SA 4.0 · source
Name	Ngo Bao Chau
Birth date	1972-06-28
Birth place	Hanoi, Vietnam
Nationality	Vietnamese
Fields	Mathematics
Alma mater	Hanoi National University of Education, Pierre and Marie Curie University
Known for	Proof of the Fundamental Lemma
Awards	Fields Medal, Vietnam Order of Merit

Ngo Bao Chau is a Vietnamese mathematician renowned for proving the Fundamental Lemma conjecture, a milestone connecting number theory and representation theory within the broader Langlands program. His work bridges techniques from algebraic geometry, automorphic forms, and harmonic analysis, influencing research at institutions such as Institut des Hautes Études Scientifiques, University of Chicago, and University of Paris VI. He received the Fields Medal for his contributions and has held visiting appointments and professorships worldwide.

Early life and education

He was born in Hanoi during the era of the Socialist Republic of Vietnam and attended the Hanoi National University of Education, where he studied under professors connected to Vietnamese mathematical traditions and international collaborations with groups at Moscow State University and Lomonosov Moscow State University. After early success in the International Mathematical Olympiad representing Vietnam, he pursued graduate studies at Pierre and Marie Curie University in Paris, entering the French mathematical community centered around the Institut des Hautes Études Scientifiques and research groups linked to École Normale Supérieure (Paris), CNRS, and Collège de France.

Academic career and positions

He completed a doctoral thesis under the supervision of advisors affiliated with Paris-Sud University and subsequently held positions at institutions including University of Chicago, Northwestern University, and University of Paris-Sud. He served as a professor at École Normale Supérieure (Paris), contributed to seminars at Institute for Advanced Study, and collaborated with researchers at Princeton University, Harvard University, Stanford University, Massachusetts Institute of Technology, and Yale University. He has been invited to give lectures at venues such as International Congress of Mathematicians, International Mathematical Union events, Clay Mathematics Institute workshops, and summer schools organized by Mathematical Sciences Research Institute and Max Planck Institute for Mathematics.

Contributions to mathematics

His principal achievement is a proof of the Fundamental Lemma conjecture within the Langlands program, connecting the theory of automorphic representations on reductive groups to Galois representations and Shimura varieties. He introduced techniques synthesizing ideas from algebraic geometry, notably the geometry of moduli spaces and perverse sheaves, with methods from harmonic analysis on p-adic groups and adelic methods used in automorphic forms theory. His work built upon and interacted with contributions by Robert Langlands, James Arthur, David Kazhdan, George Lusztig, and Pierre Deligne, and it influenced subsequent research by figures such as Edward Frenkel, Richard Taylor, Michael Harris, Ngo Dac Tuan (note different person), and Raphaël Rouquier. The proof elaborated geometric approaches related to the Hitchin fibration and used tools from Weil conjectures-inspired cohomology theories, referencing concepts developed by Alexander Grothendieck, Jean-Pierre Serre, Pierre Deligne, and Nicholas Katz. Applications of his results impact the study of L-functions, trace formulas, and correspondences conjectured by Langlands with ramifications in research at Perelman Institute and research programs at Institute des Hautes Études Scientifiques.

Awards and honors

He was awarded the Fields Medal for his proof of the Fundamental Lemma, joining laureates such as Terence Tao, Grigori Perelman (declined), Maryam Mirzakhani (posthumous), and Ngô Bảo Châu (note: subject). Other honors include national recognition from the Socialist Republic of Vietnam such as the Vietnam Order of Merit and invitations to serve on editorial boards of journals connected to Annals of Mathematics, Inventiones Mathematicae, and Journal of the American Mathematical Society. He has been a member or fellow of organizations including the International Mathematical Union, the Academia Europaea, and received prizes associated with bodies like the Clay Mathematics Institute and Sloan Foundation.

Personal life and legacy

Outside research he has participated in academic outreach linking Vietnamese institutions such as Vietnam National University, Hanoi with international centers like University of Paris, University of Chicago, and Institute for Advanced Study. His legacy appears in the continued development of the Langlands program community, influencing programs at IHÉS, MSRI, Banff International Research Station, and mentoring researchers who join faculties at Columbia University, University of Oxford, University of Cambridge, ETH Zurich, and Princeton University. His career intersects with global mathematical networks involving conferences like the International Congress of Mathematicians and collaborations across research institutes including Max Planck Institute for Mathematics and Institute of Mathematics of the Academy of Sciences of Vietnam.

Category:Vietnamese mathematicians Category:Fields Medalists