Vladimir Voevodsky

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 for a while, but was expelled without a diploma for refusing to attend classes and failing academically. He received his Ph.D. in mathematics from Harvard University in 1992 after being recommended without even applying and without a formal college degree, following several independent publications; 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.See the autobiographical story in {{cite web|last1=Voevodsky|first1=Vladimir|title=Univalent Foundations|url=http://www.math.ias.edu/~vladimir/Site3/Univalent_Foundations_files/2014_IAS.pdf|publisher=Institute for Advanced Study}}

{{Moresources|section|date=August 2023}}

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 K-theory of a field to its étale cohomology.{{cite journal|last1=Morel|first1=F.|title=Voevodsky's proof of Milnor's conjecture|journal=Bulletin of the American Mathematical Society|volume=35|issue=2|year=1998|pages=123–144|issn=0273-0979|doi=10.1090/S0273-0979-98-00745-9|doi-access=free}} For the above, he received the Fields Medal at the 24th International Congress of Mathematicians held in Beijing, China.The second medal at the same congress was received by Laurent Lafforgue

In 1998 he gave a plenary lecture (A¹-Homotopy Theory) at the International Congress of Mathematicians in Berlin.{{cite book|author=Voevodsky, Vladimir|chapter=A¹-homotopy theory|title=In: Proceedings of the International Congress of Mathematicians|volume=1|pages=579–604|year=1998|chapter-url=https://www.math.ias.edu/vladimir/sites/math.ias.edu.vladimir/files/A1_homotopy_ICM_1998_Berlin_published.pdf}} 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.

From 2002, Voevodsky was a professor at the Institute for Advanced Study in Princeton, New Jersey.

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 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.{{Citation|title=UniMath: This coq library aims to formalize a substantial body of mathematics using the univalent point of view|date=2017-10-07|url=https://github.com/UniMath/UniMath|publisher=Univalent Mathematics|access-date=2017-10-07}}

In April 2016, the University of Gothenburg awarded an honorary doctorate to Voevodsky.{{cite web|url=http://itufak.gu.se/english/current/news/news-detail/fields-medalist-vladimir-voevodsky-new-honorary-doctor-at-the-it-faculty.cid1380718|title=Fields medalist Vladimir Voevodsky new honorary doctor at the IT Faculty|date=30 June 2016 }}

Voevodsky died on 30 September 2017 at his home in Princeton, New Jersey, aged 51, from an aneurysm.{{cite news|author=Rehmeyer, Julie|date=6 October 2017|title=Vladimir Voevodsky, Revolutionary Mathematician, Dies at 51|newspaper=New York Times|url=https://www.nytimes.com/2017/10/06/obituaries/vladimir-voevodsky-revolutionary-mathematician-dies-at-51.html}}{{cite web | title=IAS: Vladimir Voevodsky, Fields Medalist, Dies at 51|date=30 September 2017 |url=https://www.ias.edu/news/2017/vladimir-voevodsky| access-date=2017-09-30}} He was survived by his daughters, Diana Yasmine Voevodsky and Natalia Dalia Shalaby.

• {{cite book|last1=Voevodsky|first1= Vladimir|last2= Suslin|first2= Andrei |author-link2=Andrei Suslin|last3=Friedlander|first3= Eric M.|author-link3=Eric Friedlander|year= 2000 |url=https://books.google.com/books?id=WiDHDgAAQBAJ|title=Cycles, transfers, and motivic homology theories|series= Annals of Mathematics Studies|volume= 143|publisher=Princeton University Press|isbn= 9781400837120}}{{cite journal|author=Weibel, Charles A.|title=Review of Cycles, transfers, and motivic homology theories by Vladimir Voevodsky, Andrei Muslin, and Eric M. Friedlander|journal=Bull. Amer. Math. Soc. (N.S.)|year=2002|volume=39|issue=1|pages=137–143|url=http://www.ams.org/journals/bull/2002-39-01/S0273-0979-01-00930-2/S0273-0979-01-00930-2.pdf|doi=10.1090/s0273-0979-01-00930-2|doi-access=free}}
• {{cite book|last1= Mazza|first1= Carlo|author-link=Carlo Mazza (mathematician)|last2= Voevodsky|first2= Vladimir|last3= Weibel|first3= Charles A.|author-link3=Charles Weibel|url =https://books.google.com/books?id=gYSeAwAAQBAJ|title='Lecture notes on motivic cohomology|series= Clay Mathematics Monographs| volume= 2|publisher=American Mathematical Society|year= 2011|isbn= 9780821853214}}[http://bookstore.ams.org/cmim-2 Lecture notes on motivic cohomology at AMS Bookstore][http://euro-math-soc.eu/review/lecture-notes-motivic-cohomology Review: Lecture Notes on Motivic Cohomology, European Mathematical Society]

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• {{cite journal |author=Friedlander |first1=Eric M. |last2=Rapoport |first2=Michael |last3=Suslin |first3=Andrei |year=2003 |title=The mathematical work of the 2002 Fields medalists |url=http://www.ams.org/notices/200302/fea-suslin.pdf |journal=Notices Amer. Math. Soc. |volume=50 |issue=2 |pages=212–217}}

• More information about his work can be found on his [https://www.math.ias.edu/vladimir/home website]

{{Sister project links| wikt=no | commons=Category:Vladimir Voevodsky | b=no | n=no | q=Vladimir Voevodsky | s=no | v=no | voy=no | species=no | d=no}}

• [https://github.com/vladimirias Vladimir Voevodsky on GitHub] Contains the slides of many of his recent lectures.
• [http://www.polit.ru/science/2006/08/22/voevod.html По большому филдсовскому счету] Интервью с Владимиром Воеводским и Лораном Лаффоргом
• Julie Rehmeyer, [https://www.nytimes.com/2017/10/06/obituaries/vladimir-voevodsky-revolutionary-mathematician-dies-at-51.html Vladimir Voevodsky, Revolutionary Mathematician, Dies at 51], New York Times, 6 October 2017
• {{MacTutor Biography|id=Voevodsky}}
• {{MathGenealogy|id=28125}}

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