Seminars Sorted by Series

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...

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: 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: 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: 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 "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...

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: I will discuss main ideas and steps in the proof of Milnor and Bloch-Kato Conjectures given by 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...

Abstract: Toposes were invented by Grothendieck to abstract properties of categories of sheaves, but soon Lawvere and Tierney realized that the elementary (i.e. "finitary" or first-order) properties satisfied by Grothendieck's toposes were precisely...

Abstract: In 1973 Steve Wilson proved the remarkable theorem that the even spaces in the loop spectrum for complex cobordism have cell decompositions with only even dimensional cells. The (conjectural) analogue of this in motivic homotopy theory...

Abstract: We reflect on mathematical efforts made years ago, initiated by Blaine Lawson and much influenced by Vladimir Voevodsky's work. In work with Lawson, Mazur, Walker, Suslin, and Haesemyer, a "semi-topological theory" for cohomology and K...

Abstract: One formal system for Voevodsky's univalent foundations is Martin-Löf's type theory. This type theory is the basis of proof assistants, such as Agda, Coq, and NuPRL, that are used not only for the formalization of mathematics, but in...

Abstract: I will review the strategy of the proof of the conservativity conjecture for the classical realisations of Voevodsky motives over a characteristic zero fields. I will also mention some other consequences of this proof such as the...