Vladimir Voevodsky

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...

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: 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: 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: 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:

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