Vladimir Alexandrovich Voevodsky (, russian: Влади́мир Алекса́ндрович Воево́дский; 4 June 1966 – 30 September 2017) was a

Russia Russia (, , ), or the Russian Federation, is a transcontinental country spanning Eastern Europe and Northern Asia. It is the largest country in the world, with its internationally recognised territory covering , and encompassing one-ei ...

America The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territori ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. His work in developing a

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topolo ...

for algebraic varieties and formulating

motivic cohomology Motivic cohomology is an invariant of algebraic varieties and of more general schemes. It is a type of cohomology related to motives and includes the Chow ring of algebraic cycles as a special case. Some of the deepest problems in algebraic geome ...

led to the award of a

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award h ...

in 2002. He is also known for the proof of the

Milnor conjecture In mathematics, the Milnor conjecture was a proposal by of a description of the Milnor K-theory (mod 2) of a general field ''F'' with characteristic different from 2, by means of the Galois (or equivalently étale) cohomology of ''F'' wi ...

and motivic Bloch–Kato conjectures and for the univalent foundations of mathematics and homotopy type theory.

Early life and education

Vladimir Voevodsky's father, Aleksander Voevodsky, was head of the Laboratory of High Energy Leptons in the Institute for Nuclear Research at the Russian Academy of Sciences. His mother Tatyana was a chemist. Voevodsky attended

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

for a while, but was forced to leave without a diploma for refusing to attend classes and failing academically. He received his Ph.D. in mathematics from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of highe ...

in 1992 after being recommended without even applying, following several independent publications, he was advised there by

David Kazhdan David Kazhdan ( he, דוד קשדן), born Dmitry Aleksandrovich Kazhdan (russian: Дми́трий Александро́вич Кажда́н), is a Soviet and Israeli mathematician known for work in representation theory. Kazhdan is a 1990 Ma ...

. While he was a first year undergraduate, he was given a copy of Esquisse d'un Programme (submitted a few months earlier by Alexander Grothendieck to

CNRS The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,63 ...

) by his advisor George Shabat. He learned the

French language French ( or ) is a Romance language of the Indo-European family. It descended from the Vulgar Latin of the Roman Empire, as did all Romance languages. French evolved from Gallo-Romance, the Latin spoken in Gaul, and more specifically in N ...

"with the sole purpose of being able to read this text" and started his research on some of the themes mentioned there.

Work

Voevodsky's work was in the intersection of

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

with

algebraic topology Algebraic topology is a branch of mathematics that 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 ...

. Along with Fabien Morel, Voevodsky introduced a

for schemes. He also formulated what is now believed to be the correct form of

, and used this new tool to prove Milnor's conjecture relating the Milnor K-theory of a field to its étale cohomology. For the above, he received the

at the 24th

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rena ...

held in

Beijing } Beijing ( ; ; ), Chinese postal romanization, alternatively romanized as Peking ( ), is the Capital city, capital of the China, People's Republic of China. It is the center of power and development of the country. Beijing is the world's Li ...

China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's List of countries and dependencies by population, most populous country, with a Population of China, population exceeding 1.4 billion, slig ...

. In 1998 he gave a plenary lecture (''A¹-Homotopy Theory'') at the International Congress of Mathematicians in

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitu ...

. He coauthored (with

Andrei Suslin Andrei Suslin (russian: Андре́й Алекса́ндрович Су́слин, sometimes transliterated Souslin) was a Russian mathematician who contributed to algebraic K-theory and its connections with algebraic geometry. He was a Trustee ...

and Eric M. Friedlander) ''Cycles, Transfers and Motivic Homology Theories'', which develops the theory of motivic cohomology in some detail. From 2002, Voevodsky was a professor at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent schola ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of w ...

. In January 2009, at an anniversary conference in honor of Alexander Grothendieck, held at the Institut des Hautes Études Scientifiques, Voevodsky announced a proof of the full Bloch–Kato conjectures. In 2009, he constructed the univalent model of

Martin-Löf type theory Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics. Intuitionistic type theory was created by Per Martin-Löf, a Swedish mathematician and p ...

in simplicial sets. This led to important advances in type theory and in the development of new univalent foundations of mathematics that Voevodsky worked on in his final years. He worked on a Coq library ''UniMath'' using univalent ideas. In April 2016, the

University of Gothenburg The University of Gothenburg ( sv, Göteborgs universitet) is a university in Sweden's second largest city, Gothenburg. Founded in 1891, the university is the third-oldest of the current Swedish universities and with 37,000 students and 6000 st ...

awarded an honorary doctorate to Voevodsky.

Death and legacy

Voevodsky died on 30 September 2017 at his home in Princeton, from an

aneurysm An aneurysm is an outward bulging, likened to a bubble or balloon, caused by a localized, abnormal, weak spot on a blood vessel wall. Aneurysms may be a result of a hereditary condition or an acquired disease. Aneurysms can also be a nidus ( ...

. He is survived by daughters Diana Yasmine Voevodsky and Natalia Dalia Shalaby.

Selected works

* *Review: ''Lecture Notes on Motivic Cohomology'', European Mathematical Society
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Notes

References

External links

Vladimir Voevodsky on GitHub
Contains the slides of many of his recent lectures.

Интервью с Владимиром Воеводским и Лораном Лаффоргом * Julie Rehmeyer

New York Times, 6 October 2017 * * {{DEFAULTSORT:Voevodsky, Vladimir 1966 births 2017 deaths 20th-century Russian mathematicians 21st-century Russian mathematicians Fields Medalists Algebraic geometers Topologists Harvard Graduate School of Arts and Sciences alumni Institute for Advanced Study faculty Soviet mathematicians Sloan Research Fellows Harvard Fellows Russian expatriates in the United States