Paul Arne Østvær is a Norwegian mathematician specialized in abstract homotopy theory. Paul Arne used Quillen model categories to study questions in algebraic topology, operator algebras and algebraic geometry. In algebraic geometry this includes $A^1$-homotopy theory, motives, and even noncommutative motives. In operator algebras he introduced a Quillen model structure on certain category of cubical presheaves on a category of operator algebras.
Homotopy theory of $C^*$-algebras, Frontiers in Mathematics, Springer Basel, 2010, (arxiv/0812.0154, pdf)
(on the model structure on operator algebras)
Markus Spitzweck, Paul Arne Østvær, Motivic twisted K-theory, arxiv/1008.4915