My recent work is available at the arXiv

Noncommutative Weil conjecture

HPD-invariance of the Tate, Beilinson and Parshin conjectures

  Schur-finiteness (and Bass-finiteness) conjecture for quadric fibrations and for families of sextic du Val del Pezzo surfaces

Jacques Tits' motivic measure

Embedding of the derived Brauer group into the secondary K-theory ring
To appear in Journal of Noncommutative Geometry

From semi-orthogonal decompositions to polarized intermediate Jacobians via Jacobians of noncommutative motives
with Marcello Bernardara
To appear in Moscow Mathematical Journal