bio

Before joining the GAPT group at Cardiff University, I was a post-doc (akademischer Rat auf Zeit) at the University of Münster. I received my PhD in Mathematics under the supervision of Thomas Schick and my Diploma in Physics under the supervision of Karl-Henning Rehren in Göttingen.

My research focuses on connections between operator algebras and algebraic topology. A topology on a space allows us to talk about closeness or neighbourhoods of points without actually having to talk about distances between them. Many geometric objects, like surfaces or higher dimensional manifolds, are topological spaces. The goal of algebraic topology is to associate algebraic invariants, often groups, rings or modules, to these spaces in a natural way to distinguish them up to homotopy equivalence, i.e. up to continuous deformations.

An important example of such an invariant is topological K-theory. It is a generalised cohomology theory, which means that it satisfies axioms that allow its computation from a decomposition of the space into smaller parts. It can be defined as an invariant associated to the algebra of continuous functions on the space (vanishing at infinity) and as such it can be generalised to noncommutative operator algebras. These algebras not only play an important role in mathematical physics, they also can be used to describe highly singular topological spaces, like orbifolds or foliations.

K-theory has many different variants, e.g. equivariant K-theory or twisted K-theory. The outcome of one of my research projects, which was joint work with Marius Dadarlat, was a description of twisted K-theory via operator algebras that includes the higher twists, a feature of the theory, which was formerly only accessible via homotopy theory. ​ I am interested in these and other interactions between algebraic topology, homotopy theory and operator algebras. Since I studied mathematical physics before my PhD, I am also interested in topological and conformal field theories and their connection with another generalised cohomology theory, called elliptic cohomology.

academic positions

  • 08/2019 – present — Senior Lecturer, Cardiff University
  • 04/2016 – 07/2019 — Lecturer, Cardiff University
  • 11/2010 – 03/2016 — Akademischer Rat auf Zeit, University of Münster
  • 08/2010 – 10/2010 — Research Assistant, University of Münster
  • 12/2009 – 07/2010 — Akademischer Rat auf Zeit, University of Göttingen
  • 09/2009 – 11/2009 — Research Assistant, Courant Research Center, Göttingen

education

  • 07/2016 — Habilitation in Mathematics, University of Münster
  • 08/2009 — Dr. rer. nat. in Mathematics (summa cum laude), University of Göttingen
  • 05/2006 — Diploma in Theoretical Physics, University of Göttingen
  • 06/1999 — Abitur, Liebfrauenschule Cloppenburg

prizes and scholarships

  • 2026 — Outstanding Paper Prize, Journal of the Mathematical Society of Japan (JMSJ)
  • 2017 — Nomination for the Philip Leverhulme Prize
  • 2010 — Dissertation Prize 2009, Universitätsbund Göttingen
  • 2006–2009 — PhD Scholarship, Studienstiftung des deutschen Volkes (German National Academic Foundation)
  • 2003–2006 — Diplom Scholarship, Studienstiftung des deutschen Volkes