Vladimir Voevodsky

Abstract: It was observed for a while (at least, since the times of E.Witt) that the notion of anisotropy of an algebraic variety (that is, the absence of points of degree prime to a given p on it) plays an important role (most notably, in the...

Homotopy type theory provides a “synthetic” framework that is suitable for developing the theory of mathematical objects with natively homotopical content. A famous example is given by (∞,1)-categories — aka “∞-categories” — which are categories...

Abstract: The "equivalence principle" says that meaningful statements in mathematics should be invariant under the appropriate notion of equivalence of the objects under consideration. In set-theoretic foundations, the EP is not enforced; e.g., the...

Abstract: The talk will start with discussing the common features of the three mathematicians from the title: their non-standard education and specific relations with the community, outstanding imagination, productivity and contribution to the...

Abstract: The discovery of the "univalence principle" is a mark of Voevodsky's genius. Its importance for type theory cannot be overestimated: it is like the "induction principle" for arithmetic. I will recall the homotopy interpretation of type...

Abstract: This talk will be a survey on the development of $A^1$-homotopy theory, from its genesis, and my meeting with Vladimir, to its first successes, to more recent achievements and to some remaining open problems and potential developments.

Abstract: In the univalent foundation formalism, equality makes sense only between objects of the same type, and is itself a type. We will explain that this is closer to mathematical practice than the Zermelo-Fraenkel notion of equality is.

Abstract: Vladimir Voevodsky was a brilliant mathematician, a Fields Medal winner, and a faculty member at the Institute for Advanced Study, until his sudden and unexpected death in 2017 at the age of 51. He had a special flair for thinking...

https://www.ias.edu/events/gathering-remembrance-vladimir-voevodsky https://www.ias.edu/ideas/2017/remembering-vladimir-voevodsky https://www.ias.edu/news/in-the-media/2017/voevodsky-obit-nyt For photos of the Remembrance: https://www.flickr.com...

In Voevodsky’s experience, the work of a mathematician is 5% creative insight and 95% self-verification. Moreover, the more original the insight, the more one has to pay for it later in self-verification work. The Univalent Foundations project...