Владимир Воеводский (who published in English as Vladimir Voevodsky) was a Russian mathematician working in the Institute for Advanced Study.
Voevodsky received a Fields medal in 2002 for a proof of the Milnor conjecture. The proof crucially uses A1-homotopy theory and motivic cohomology developed by Voevodsky for this purpose. In further development of this in 2009 Voevodsky announced a proof of the Bloch-Kato conjecture.
After this work in algebraic geometry, cohomology and homotopy theory Voevodsky turned to the foundations of mathematics and worked on homotopy type theory which he described as a new “univalent foundations” for modern mathematics with its emphasis on homotopy theory and higher category theory.
Introducing the modern notion of equivalence in type theory (namely via contractible fibers) and thereby fixing the univalence axiom of Hofmann & Streicher (1998), §5.4 (due to the subtlety with quasi-inverses):
Proposal for a “Homotopy Type System” (cf. semisimplicial type):
Vladimir Voevodsky, A type system with two kinds of identity types (Feb. 2013) [pdf]
Vladimir Voevodsky, A simple type system (Jan 2013) [pdf, Implementation]
The origins and motivations for univalent foundations, IAS 2014 (adapted transcript, video)
list of video-recorded talks on homotopy type theory: here.
An interview is here.
Roman Mikhailov, Интервью Владимира Воеводского, Princeton 2012 (Part 1, Part 2)
Le bifurcation de Vladimir Voevodsky, interview conducted by Fondation Sciences Mathématiques de Paris, 2014, video, transcript in French.
Last revised on July 13, 2023 at 14:43:23. See the history of this page for a list of all contributions to it.