Vladimir Voevodsky

Vladimir Alexandrovich Voevodsky (/vɔɪˈvɒdski/; Russian: Влади́мир Алекса́ндрович Воево́дский, born 4 June 1966) is a Russian mathematician. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal in 2002. He is also known for the proof of the Milnor conjecture and motivic Bloch-Kato conjectures and for the univalent foundations of mathematics and homotopy type theory.

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 was a chemist. Voevodsky attended Moscow State University and received his Ph.D. in mathematics from Harvard University in 1992, advised by David Kazhdan. Currently he is a full professor at the Institute for Advanced Study in Princeton, New Jersey.

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) by his advisor George Shabat. He learnt the French language "with the sole purpose of being able to read this text" and started his research on some of the themes mentioned there.

Voevodsky's work is in the intersection of algebraic geometry with algebraic topology. Along with Fabien Morel, Voevodsky introduced a homotopy theory for schemes. He also formulated what is now believed to be the correct form of motivic cohomology, 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 Fields Medal at the 24th International Congress of Mathematicians held in Beijing, China.

He is coauthor (with Andrei Suslin 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 about Alexander Grothendieck, Voevodsky announced a proof of the full Bloch-Kato conjectures.

In 2009 he constructed the univalent model of Martin-Löf type theory in simplicial sets. This led to important advances in type theory and in the development of new Univalent foundations of mathematics that Voevodsky is currently working on.

In April 2016 the University of Gothenburg decided to award an honorary doctorate to Voevodsky.

• Voevodsky, Vladimir, Suslin, Andrei, and Friedlander, Eric M. (2000). Cycles, transfers, and motivic homology theories. Annals of Mathematics Studies Vol. 143. Princeton University Press.