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...