Vladimir Voevodsky
Vladimir Voevodsky  

Voevodsky in 2011


Born 
Vladimir Alexandrovich Voevodsky 4 June 1966 Moscow, Soviet Union 
Died 
30 September 2017 (aged 51) Princeton, New Jersey, United States 
Nationality  Russian, American 
Alma mater 
Moscow State University Harvard University 
Awards  Fields Medal (2002) 
Scientific career  
Fields  Mathematics 
Institutions  Institute for Advanced Study 
Doctoral advisor  David Kazhdan 
Vladimir Alexandrovich Voevodsky (/vɔɪˈvɒdski/; Russian: Влади́мир Алекса́ндрович Воево́дский, 4 June 1966 – 30 September 2017) was 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 BlochKato conjectures and for the univalent foundations of mathematics and homotopy type theory.
Contents
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.^{[1]} Voevodsky attended Moscow State University and left without a diploma after flunking out of college.^{[1]} He received his Ph.D. in mathematics from Harvard University in 1992 after being recommended without ever applying, following several independent publications;^{[1]} he was advised there by David Kazhdan.
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 learned 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.^{[2]}
Work
Voevodsky's work was 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 Ktheory 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.^{[3]}
In 1998 he gave a plenary lecture (A^{1}Homotopy Theory) at the International Congress of Mathematicians in Berlin.^{[4]} He coauthored (with Andrei Suslin and Eric M. Friedlander) 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 BlochKato conjectures.
In 2009, he constructed the univalent model of MartinLöf 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 worked on in his final years. He worked on a Coq library UniMath using univalent ideas.^{[1]}^{[5]}
In April 2016, University of Gothenburg awarded an honorary doctorate to Voevodsky.^{[6]}
Death and legacy
Voevodsky was a full professor at the Institute for Advanced Study in Princeton, New Jersey, at the time of his death. Voevodsky died on 30 September 2017 at his home in Princeton.^{[1]}^{[7]} He is survived by daughters Diana Yasmine Voevodsky and Natalia Dalia Shalby.^{[1]}
Selected works
 Voevodsky, Vladimir, Suslin, Andrei, and Friedlander, Eric M. (2000). Cycles, transfers, and motivic homology theories. Annals of Mathematics Studies Vol. 143. Princeton University Press.^{[8]}
 Mazza, Carlo, Voevodsky, Vladimir and Weibel, Charles A. Lecture notes on motivic cohomology. Clay Mathematical Monnographs, Vol. 2. American Mathematical Soc., 2011^{[9]}^{[10]}
Notes
 ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} Rehmeyer, Julie (6 October 2017). "Vladimir Voevodsky, Revolutionary Mathematician, Dies at 51". New York Times.
 ^ See the autobiographical story in Voevodsky, Vladimir. "Univalent Foundations" (PDF). Institute for Advanced Study.
 ^ The second medal at the same congress was received by Laurent Lafforgue
 ^ Voevodsky, Vladimir (1998). "A1homotopy theory" (PDF). In: Proceedings of the International Congress of Mathematicians. vol. 1. pp. 579–604.
 ^ UniMath: This coq library aims to formalize a substantial body of mathematics using the univalent point of view, Univalent Mathematics, 20171007, retrieved 20171007
 ^ "Fields medalist Vladimir Voevodsky new honorary doctor at the IT Faculty".
 ^ "IAS: Vladimir Voevodsky, Fields Medalist, Dies at 51". Retrieved 20170930.
 ^ Weibel, Charles A. (2002). "Review of Cycles, transfers, and motivic homology theories by Vladimir Voevodsky, Andrei Muslin, and Eric M. Friedlander" (PDF). Bull. Amer. Math. Soc. (N.S.). 39 (1): 137–143.
 ^ Lecture notes on motivic cohomology at AMS Bookstore
 ^ Review: Lecture Notes on Motivic Cohomology, European Mathematical Society
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.
Further reading
 More information about his work can be found on his website
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
 Julie Rehmeyer, Vladimir Voevodsky, Revolutionary Mathematician, Dies at 51, New York Times, 6 October 2017
 O'Connor, John J.; Robertson, Edmund F., "Vladimir Voevodsky", MacTutor History of Mathematics archive, University of St Andrews.
 Vladimir Voevodsky at the Mathematics Genealogy Project
 1966 births
 2017 deaths
 20thcentury mathematicians
 21stcentury mathematicians
 Russian mathematicians
 Fields Medalists
 Algebraic geometers
 Topologists
 Harvard University alumni
 Institute for Advanced Study faculty
 Soviet mathematicians
 Sloan Research Fellows
 Harvard Fellows
 Russian expatriates in the United States