Vladimir Voevodsky

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Vladimir Voevodsky
VladimirVoevodsky.jpg
Born (1966-06-04) 4 June 1966 (age 48)
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 mathematician who was born in Moscow, USSR and lived, studied and worked there until 1990. 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 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.

Biography[edit]

Vladimir Voevodsky's father, Aleksandr Voevodsky, was head of the Laboratory of High Energy Leptons in the Institute for Nuclear Research at the Russian Academy of Sciences. His mother is 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.

Work[edit]

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-Lof type theory in simplicial sets. This was a major step in the development of homotopy type theory, and led to his programme of using it as a foundation for all mathematics. In such a role he calls it univalent foundations.

References[edit]

  • 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[edit]