A noncommutative approach to the celebrated conjectures of Grothendieck, Voevodsky and Tate

The Grothendieck standard conjectures, the Voevodsky nilpotence conjecture, and also the Tate conjecture, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of these celebrated conjectures remains elusive. The aim of this talk is to give an overview of a recent noncommutative approach which has led to the proof of the aforementioned important conjectures in several new cases.