Vladimir Voevodsky

Vladimir Voevodsky
Born	(1966-06-04) 4 June 1966 Moscow, Soviet Union
Nationality	Russian
Fields	Mathematics
Institutions	Institute for Advanced Study
Alma mater	Moscow State University Harvard University
Doctoral advisor	David Kazhdan
Notable awards	Fields Medal (2002)

Vladimir Voevodsky (Russian: Владимир Александрович Воеводский, 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. More information about his work can be found on his website.

Biography

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 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.

Work

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, together with Laurent Lafforgue, 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 the Martin-Löf type theory in simplicial sets. This led to important advances in the development of new foundations of mathematics that Voevodsky is working on.

References

• Friedlander, Eric M., Rapoport, Michael, and Suslin, Andrei. (2003) "The mathematical work of the 2002 Fields medalists". Notices Amer. Math. Soc. 50 (2), 212–217.
• Voevodsky, Vladimir, Suslin, Andrei, and Friedlander, Eric M. (2000) Cycles, transfers, and motivic homology theories. Annals of Mathematics Studies Vol. 143. Princeton University Press.

External links

• Vladimir Voevodsky on GitHub Contains the slides of many of his recent lectures.
• По большому филдсовскому счету Интервью с Владимиром Воеводским и Лораном Лаффоргом
• .
• Vladimir Voevodsky at the Mathematics Genealogy Project