Vladimir Voevodsky is a Russian

Russians

The Russian people are an East Slavic ethnic group native to Russia, speaking the Russian language and primarily living in Russia and neighboring countries....

 American

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 mathematician

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....

. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology

Motivic cohomology

Motivic cohomology is a cohomological theory in mathematics, the existence of which was first conjectured by Alexander Grothendieck during the 1960s. At that time, it was conceived as a theory constructed on the basis of the so-called standard conjectures on algebraic cycles, in algebraic geometry...

 led to the award of a 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...

 in 2002.

Biography

Voevodsky attended Moscow State University

Moscow State University

Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...

 and received his Ph.D.

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 mathematics from Harvard University

Harvard University

Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...

 in 1992, advised by David Kazhdan

David Kazhdan

David Kazhdan or Každan, Kazhdan, formerly named Dmitry Aleksandrovich Kazhdan , is a Soviet and Israeli mathematician known for work in representation theory.-Life:...

. Currently he is a full professor 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...

 in 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...

.

Work

Voevodsky's work is in the intersection of algebraic geometry

Algebraic geometry

Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...

 with algebraic topology

Algebraic topology

Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.Although algebraic topology...

. Along with Fabien Morel, Voevodsky introduced a homotopy theory for schemes

Scheme (mathematics)

In mathematics, a scheme is an important concept connecting the fields of algebraic geometry, commutative algebra and number theory. Schemes were introduced by Alexander Grothendieck so as to broaden the notion of algebraic variety; some consider schemes to be the basic object of study of modern...

. He also formulated what is now believed to be the correct form of motivic cohomology

Motivic cohomology

Motivic cohomology is a cohomological theory in mathematics, the existence of which was first conjectured by Alexander Grothendieck during the 1960s. At that time, it was conceived as a theory constructed on the basis of the so-called standard conjectures on algebraic cycles, in algebraic geometry...

, and used this new tool to prove Milnor's conjecture relating the Milnor K-theory

K-theory

In mathematics, K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It...

 of a field

Field (mathematics)

In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it is an algebraic structure with notions of addition, subtraction, multiplication, and division, satisfying certain axioms...

 to its étale cohomology

Étale cohomology

In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures...

. For the above, 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...

, together with Laurent Lafforgue

Laurent Lafforgue

Laurent Lafforgue is a French mathematician.He won 2 silver medals at International Mathematical Olympiad in 1984 and 1985....

, at the 24th International Congress of Mathematicians held in Beijing

Beijing

Beijing , also known as Peking , is the capital of the People's Republic of China and one of the most populous cities in the world, with a population of 19,612,368 as of 2010. The city is the country's political, cultural, and educational center, and home to the headquarters for most of China's...

, China

China

Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...

.

He is coauthor (with Andrei Suslin

Andrei Suslin

Andrei Suslin is a Russian mathematician who has made major contributions to the field of algebra, especially algebraic K-theory and its connections with algebraic geometry. He is currently a Trustee Chair and Professor of mathematics at Northwestern University.He was born on December 27, 1950,...

 and Eric M. Friedlander) of Cycles, Transfers and Motivic Homology Theories, which develops the theory of motivic cohomology in some detail.

In January 2009, at an IHES anniversary conference for Alexander Grothendieck

Alexander Grothendieck

Alexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...

, Voevodsky announced a proof of the full Bloch-Kato conjectures.

External links

• По большому филдсовскому счету Интервью с Владимиром Воеводским и Лораном Лаффоргом