Ngo Bao Chau
Encyclopedia
Ngô Bảo Châu ŋo ɓa᷉ːʊ̯ cəʊ̯ (born June 28, 1972) is a Vietnamese and French mathematician
at the University of Chicago
, best known for proving the fundamental lemma for automorphic forms proposed by Robert Langlands
and Diana Shelstad
. He is the first Vietnamese to receive the Fields Medal.
, North Vietnam
. His father, professor Ngo Huy Can, is full professor of Physics at the Vietnam National Institute of Mechanics. His mother, Tran Luu Van Hien, is a physician and associate professor at an herbal medicine hospital in Hanoi.
At age 15, he entered the mathematics concentration class at Vietnam National University
High School (Khối chuyên Tổng Hợp – Đại học Khoa Học Tự Nhiên Hà Nội), formerly known as A0-class. In grades 11 and 12, Chau participated in the 29th and 30th International Mathematical Olympiad
(IMO) and became the first Vietnamese student to win two IMO gold medals, of which the first one was won with a perfect score (42/42).
After high school, Chau expected to study in Budapest
, but in the aftermath of the fall of Communism in Eastern Europe, the new Hungarian
government halted scholarships to students from Vietnam. After visiting Ngo's father, Paul Germain
, secretary of the French Academy of Sciences
, arranged for Ngo to study in France. He was offered a scholarship by the French government for undergraduate study at the Paris VI University but he chose the prestigious École Normale Supérieure
. He obtained a PhD
in 1997 from the Universite Paris-Sud under the supervision of Gérard Laumon
. He became a member of CNRS at Paris 13 University
from 1998 to 2005, and defended his habilitation
degree there in 2003.
He became Professor at Paris-Sud 11 University
in 2005. In 2005, at age 33, Chau received the title of professor in Vietnam and thus became the country's youngest professor ever. Since 2007, Chau has worked at the Institute for Advanced Study
, Princeton, New Jersey
as well as the Hanoi Institute of Mathematics. He joined the mathematics faculty at the University of Chicago
on September 1, 2010. Before he received his Field Medal, he was in a hurry to request French citizenship because he wanted to give recognition to French mathematics, because France is where his higher education took place. He holds both Vietnamese and French citizenship.
, the fundamental lemma for unitary group
s. Their general strategy was to understand the local orbital integral
s appearing in the fundamental lemma in terms of affine Springer fibers arising in the Hitchin fibration. This allowed them to employ the tools of geometric representation theory, namely the theory of perverse sheaves, to study what was initially a combinatorial
problem of a number-theoretic
nature. Chau eventually succeeded in formulating the proof for the fundamental lemma for Lie algebra
s in 2008. Together with results from Jean-Loup Waldspurger
, who had earlier deduced stronger forms of the fundamental lemma from this result, this completed the proof of the fundamental lemma in all cases.
for their achievement in solving the fundamental lemma proposed by Robert Langlands
for the case of unitary group
s. Chau also became the youngest professor in Vietnam in 2005. His proof of the general case was selected by Time
as one of the Top Ten Scientific Discoveries of 2009. In 2010, he received the Fields Medal
.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
, best known for proving the fundamental lemma for automorphic forms proposed by Robert Langlands
Robert Langlands
Robert Phelan Langlands is a mathematician, best known as the founder of the Langlands program. He is an emeritus professor at the Institute for Advanced Study...
and Diana Shelstad
Diana Shelstad
Diana Frost Shelstad is a mathematician known for her work in automorphic forms. She is a professor at Rutgers–Newark. She earned her doctorate at Yale University in 1974 studying real reductive algebraic groups.-Research :...
. He is the first Vietnamese to receive the Fields Medal.
Biography
Chau was born in 1972, the only son of an intellectual family in HanoiHanoi
Hanoi , is the capital of Vietnam and the country's second largest city. Its population in 2009 was estimated at 2.6 million for urban districts, 6.5 million for the metropolitan jurisdiction. From 1010 until 1802, it was the most important political centre of Vietnam...
, North Vietnam
North Vietnam
The Democratic Republic of Vietnam , was a communist state that ruled the northern half of Vietnam from 1954 until 1976 following the Geneva Conference and laid claim to all of Vietnam from 1945 to 1954 during the First Indochina War, during which they controlled pockets of territory throughout...
. His father, professor Ngo Huy Can, is full professor of Physics at the Vietnam National Institute of Mechanics. His mother, Tran Luu Van Hien, is a physician and associate professor at an herbal medicine hospital in Hanoi.
At age 15, he entered the mathematics concentration class at Vietnam National University
Vietnam National University
Vietnam National University may refer to:* Vietnam National University, Hanoi* Vietnam National University, Ho Chi Minh City...
High School (Khối chuyên Tổng Hợp – Đại học Khoa Học Tự Nhiên Hà Nội), formerly known as A0-class. In grades 11 and 12, Chau participated in the 29th and 30th International Mathematical Olympiad
International Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...
(IMO) and became the first Vietnamese student to win two IMO gold medals, of which the first one was won with a perfect score (42/42).
After high school, Chau expected to study in Budapest
Budapest
Budapest is the capital of Hungary. As the largest city of Hungary, it is the country's principal political, cultural, commercial, industrial, and transportation centre. In 2011, Budapest had 1,733,685 inhabitants, down from its 1989 peak of 2,113,645 due to suburbanization. The Budapest Commuter...
, but in the aftermath of the fall of Communism in Eastern Europe, the new Hungarian
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
government halted scholarships to students from Vietnam. After visiting Ngo's father, Paul Germain
Paul Germain
Paul Germain is an American animation screenwriter and producer. Among the shows Germain has written and/or produced for are Rugrats, All Grown Up!, The Simpsons, Recess, Even Stevens, Lloyd in Space, The Tracey Ullman Show, and Beethoven: The Animated Series...
, secretary of the French Academy of Sciences
French Academy of Sciences
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
, arranged for Ngo to study in France. He was offered a scholarship by the French government for undergraduate study at the Paris VI University but he chose the prestigious École Normale Supérieure
École Normale Supérieure
The École normale supérieure is one of the most prestigious French grandes écoles...
. He obtained a PhD
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in 1997 from the Universite Paris-Sud under the supervision of Gérard Laumon
Gérard Laumon
Gérard Laumon is a French mathematician. He studied at the École Normale Supérieure and Paris-Sud 11 University, Orsay.In 2004 Laumon and Ngô Bảo Châu received the Clay Research Award for the proof of the Langlands and Shelstad's Fundamental Lemma for unitary groups, a key component in the...
. He became a member of CNRS at Paris 13 University
Paris 13 University
University of Paris 13 is one of the thirteen universities in Paris which replaced the University of Paris in 1970. It is also identified as University of Paris North .-External links:*...
from 1998 to 2005, and defended his habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
degree there in 2003.
He became Professor at Paris-Sud 11 University
Paris-Sud 11 University
University of Paris-Sud or University of Paris-Sud or University of Paris XI is a French university distributed among several campuses in the southern suburb of Paris...
in 2005. In 2005, at age 33, Chau received the title of professor in Vietnam and thus became the country's youngest professor ever. Since 2007, Chau has worked at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
, Princeton, New Jersey
Princeton, New Jersey
Princeton is a community located in Mercer County, New Jersey, United States. It is best known as the location of Princeton University, which has been sited in the community since 1756...
as well as the Hanoi Institute of Mathematics. He joined the mathematics faculty at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
on September 1, 2010. Before he received his Field Medal, he was in a hurry to request French citizenship because he wanted to give recognition to French mathematics, because France is where his higher education took place. He holds both Vietnamese and French citizenship.
Work
Chau first came to prominence by proving, in joint work with Gérard LaumonGérard Laumon
Gérard Laumon is a French mathematician. He studied at the École Normale Supérieure and Paris-Sud 11 University, Orsay.In 2004 Laumon and Ngô Bảo Châu received the Clay Research Award for the proof of the Langlands and Shelstad's Fundamental Lemma for unitary groups, a key component in the...
, the fundamental lemma for unitary group
Unitary group
In mathematics, the unitary group of degree n, denoted U, is the group of n×n unitary matrices, with the group operation that of matrix multiplication. The unitary group is a subgroup of the general linear group GL...
s. Their general strategy was to understand the local orbital integral
Orbital integral
In mathematics, an orbital integral is an integral transform that generalizes the spherical mean operator to homogeneous spaces. Instead of integrating over spheres, one integrates over generalized spheres: for a homogeneous space X = G/H, a generalized sphere centered at a point x0 is...
s appearing in the fundamental lemma in terms of affine Springer fibers arising in the Hitchin fibration. This allowed them to employ the tools of geometric representation theory, namely the theory of perverse sheaves, to study what was initially a combinatorial
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
problem of a number-theoretic
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
nature. Chau eventually succeeded in formulating the proof for the fundamental lemma for Lie algebra
Lie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
s in 2008. Together with results from Jean-Loup Waldspurger
Jean-Loup Waldspurger
Jean-Loup Waldspurger is a French mathematician working on the Langlands program and related areas.Waldspurger attained his doctorate at École normale supérieure in 1980, under supervision of Marie-France Vignéras. He was awarded the 2009 Clay Research Award for his results in p-adic harmonic...
, who had earlier deduced stronger forms of the fundamental lemma from this result, this completed the proof of the fundamental lemma in all cases.
Honors
In 2004, Chau and Laumon were awarded the Clay Research AwardClay Research Award
The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research...
for their achievement in solving the fundamental lemma proposed by Robert Langlands
Robert Langlands
Robert Phelan Langlands is a mathematician, best known as the founder of the Langlands program. He is an emeritus professor at the Institute for Advanced Study...
for the case of unitary group
Unitary group
In mathematics, the unitary group of degree n, denoted U, is the group of n×n unitary matrices, with the group operation that of matrix multiplication. The unitary group is a subgroup of the general linear group GL...
s. Chau also became the youngest professor in Vietnam in 2005. His proof of the general case was selected by Time
Time (magazine)
Time is an American news magazine. A European edition is published from London. Time Europe covers the Middle East, Africa and, since 2003, Latin America. An Asian edition is based in Hong Kong...
as one of the Top Ten Scientific Discoveries of 2009. In 2010, he received the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
.