### Ngô Bảo Châu

Born 28 June 1972, Hanoi, Vietnam

Fields Medal (2010) “for his proof of the Fundamental Lemma in the theory of automorphic forms through the introduction of new algebro-geometric methods.”

Ngô was born into an intellectual family. His father is a professor of physics at the Vietnam National Institute of Mechanics, while his mother is a professor in a hospital specializing in naturopathy in Hanoi. Aged 15, Ngô was moved to a special class of mathematically gifted students supervised by the University of Hanoi. He participated in two international mathematics olympiads and won back-to-back golds, which had never been achieved by a Vietnamese student. After school Ngô intended to study in Budapest, but after the collapse of communism in Eastern Europe, the new Hungarian government stopped all scholarships for students from Vietnam. So the French government offered him an undergraduate place in Paris. Ngô came to France in 1990 and studied from 1992 to 1995 at the École Normale Supérieure and the University of Paris VI. In 1997 he received his doctorate under the supervision of Gérard Laumon at the University of Paris-South in Orsay with a work entitled ‘Le Lemme fondamentale de Jacquet et Ye’. After his Ph.D. he became Chargé de Recherches du CNRS (Centre National de la Recherche Scientifique) at the University of Paris-North. After his habilitation in 2003, he accepted a professorship at the University of Paris-South (2004). In 2005, Ngô became a professor in Vietnam – at the age of 33 the youngest professor in the country. From 2007, he was a Fellow of the Institute for Advanced Study at Princeton and at the same time Professor at the Hanoi Institute of Mathematics. In 2010 he moved to the Faculty of Mathematics of the University of Chicago. Since 2011, Ngô has also been Scientific Director of the newly-established Vietnam Institute for Advanced Study in Mathematics.

Ngô Bảo Châu won the 2004 Clay Research Award (with Gérard Laumon), the 2007 Oberwolfach Prize and the Sophie Germain Prize. He holds an honorary doctorate from the Vietnamese National University and is Fellow of the American Mathematical Society. In 2012 Ngô was inducted into the French Legion of Honour.

Ngô Bảo Châu’s research field is number theory, focusing in particular on Langlands program, a set of conjectures which connects number theory, representation theory of groups (a part of algebra) and algebraic geometry. More precisely, it is about how to express symmetries by means of a certain class of mappings of the complex plane, known as automorphic forms, which reflect patterns in the integers.

The Langlands program is a research program named after the Canadian mathematician Robert Langlands, who created it in the late 1960s and expanded it over the following years.

The Langlands program contains a central tool, called the Selberg trace formula after its discoverer, number theorist Atle Selberg. This formula bridges the gap between arithmetic and number theory and geometry. However, to use the trace formula, an auxiliary theorem is needed, a ‘lemma’, introduced by Langlands in 1979. He himself tried to prove it over several years without success. In 2008, Ngô Bảo Châu published a proof for a general form of this ‘fundamental lemma’ – actually one of the most important theorems of modern mathematics. He had already demonstrated previously a special case of the lemma together with Gérard Laumon.