1) Topological K- and Algebraic L-theory of C*-algebras and their relation to higher Grothendieck-Witt theory
2) The algebraic topology of manifolds, particularly of high dimensional ones
3) (Stable) Classification of 4-manifolds
1) The Analytical Assembly map and Index theory, Journal of Noncommutative geometry, Volume 9, Issue 2, (2015). Here is the arxiv version.
2) Stable Classification of 4-manifolds with 3-manifold fundamental group. Journal of Topology, Volume 10, Issue 3, (2017). This is joint with Daniel Kasprowski, Peter Teichner and Mark Powell. Here is the arxiv version.
3) Localization of Cofibration categories and groupoid C*-algebras. Algebraic & Geometric Topology, Volume 17, Issue 5, (2017). This is joint with Thomas Nikolaus and Karol Szumiło. Here is the arxiv version.
4) On the relation between K- and L-theory of C*-algebras. Mathematische Annalen, published online DOI 10.1007/s00208-017-1617-0 (2017). This is joint with Thomas Nikolaus. Here is the arxiv version.
5) A Vanishing theorem for tautological classes of aspherical manifolds. This is joint with Fabian Hebestreit, Wolfgang Lück and Oscar Randal-Williams. Here is the arxiv version. Submitted for publication.