Vladimir Voevodsky

Template:Short description Template:Infobox scientist Vladimir Alexandrovich Voevodsky (Template:IPAc-en, Template:Langx; 4 June 1966 – 30 September 2017) was a Russian-American 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.

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.<ref name=Obit/> Voevodsky attended Moscow State University for a while, but was expelled without a diploma for refusing to attend classes and failing academically.<ref name=Obit/> 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;<ref name=Obit/> 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.<ref>See the autobiographical story in Template:Cite web</ref>

Work

Template:Moresources 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.<ref name="Morel1998">Template:Cite journal</ref> For the above, he received the Fields Medal at the 24th International Congress of Mathematicians held in Beijing, China.<ref>The second medal at the same congress was received by Laurent Lafforgue</ref>

In 1998 he gave a plenary lecture (A¹-Homotopy Theory) at the International Congress of Mathematicians in Berlin.<ref>Template:Cite book</ref> 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.<ref name=Obit /><ref>Template:Citation</ref>

In April 2016, the University of Gothenburg awarded an honorary doctorate to Voevodsky.<ref>Template:Cite web</ref>

Death and legacy

Voevodsky died on 30 September 2017 at his home in Princeton, New Jersey, aged 51, from an aneurysm.<ref name=Obit>Template:Cite news</ref><ref name=ias>Template:Cite web</ref> He was survived by his daughters, Diana Yasmine Voevodsky and Natalia Dalia Shalaby.<ref name="Obit"/>

Selected works

• Template:Cite book<ref>Template:Cite journal</ref>
• Template:Cite book<ref>Lecture notes on motivic cohomology at AMS Bookstore</ref><ref>Review: Lecture Notes on Motivic Cohomology, European Mathematical Society</ref>

References

• Template:Cite journal

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
• Template:MacTutor Biography
• Template:MathGenealogy