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.

## Selected writings

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):

## Selected Interviews

category: people

Last revised on December 27, 2022 at 16:58:09. See the history of this page for a list of all contributions to it.