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
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
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...