Mathematical Institute of the University of Bonn

Dr. Koen van den Dungen (Privatdozent)

Research interests

Noncommutative geometry and unbounded KK-theory, in particular with applications to:

• the study of Fredholm operators, spectral flow, and index theory;
• (classical and quantum) gauge theories and Lorentzian geometry.

Current Teaching

Winter semester 2026-2027:

• Graduate Seminar on Global Analysis: K-homology of C*-algebras.
  Overview
  Please note that, due to a leave of absence, there will be no preliminary meeting at the end of the summer semester 2026. All information (including registration details) can be found in the Overview.

See also my Past Teaching.

Publications

(See also: ORCID, SCOPUS, arXiv, Google Scholar.)

2026: Analytic index theory and spectral flow in real Hilbert C*-modules (with Chris Bourne, Alan L. Carey, and Adam Rennie). arXiv:2606.31322

2026: A K-theoretic note on the spectral localiser. arXiv:2602.20961

2025: Fredholm complexes of Hilbert C*-modules (with Brian Villegas-Villalpando). arXiv:2505.07568

2025: Dirac-Schrödinger operators, index theory and spectral flow. Journal of the London Mathematical Society 112 (2025), e70301. (doi, arXiv)

2025: Generalised Dirac-Schrödinger operators and the Callias Theorem. Forum of Mathematics, Sigma (2025), Vol. 13:e11 1-29. (doi, arXiv)

2023: Localisations of half-closed modules and the unbounded Kasparov product. International Mathematics Research Notices, 2023, Issue 9, 7578-7615. (doi, arXiv)

2023: The intersection of complemented submodules is not complemented. Addendum to: "The Friedrichs angle and alternating projections in Hilbert C*-modules" [J. Math. Anal. Appl. 516 (2022) 126474] (with Bram Mesland and Adam Rennie). Journal of Mathematical Analysis and Applications 522 (2023), 127002. (doi, arXiv)

2022: The Kasparov product on submersions of open manifolds. Journal of Topology and Analysis 14 (2022), 147-181. (doi, arXiv)

2021: The APS-index and the spectral flow (with Lennart Ronge). Operators and Matrices 15 (2021), 1393-1416. (doi, arXiv)

2020: Homotopy equivalence in unbounded KK-theory (with Bram Mesland). Annals of K-theory 5 (2020), 501-537. (doi, arXiv)

2019: The index of generalised Dirac-Schrödinger operators. Journal of Spectral Theory 9 (2019), 1459-1506. (doi, arXiv)

2019: Addendum to: Indefinite Kasparov modules and pseudo-Riemannian manifolds. Annales Henri Poincaré 20 (2019), 3007-3017. (doi, arXiv)

2019: A perspective from (unbounded) KK-theory. Appendix to: The spectral flow of a family of Toeplitz operators (by Maxim Braverman). Letters in Mathematical Physics 109 (2019), 2271-2289. (doi, arXiv)

2018: Locally bounded perturbations and (odd) unbounded KK-theory. Journal of Noncommutative Geometry 12 (2018), 1445-1467. (doi, arXiv)

2018: Families of spectral triples and foliations of space(time). Journal of Mathematical Physics 59 (2018), 063507. (doi, arXiv)

2016: Indefinite Kasparov modules and pseudo-Riemannian manifolds (with Adam Rennie). Annales Henri Poincaré 17 (2016), 3255-3286. (doi, arXiv)

2016: Krein spectral triples and the fermionic action. Mathematical Physics, Analysis and Geometry 19:4 (2016). (doi, arXiv)

2014: On globally non-trivial almost-commutative manifolds (with Jord Boeijink). Journal of Mathematical Physics 55, 103508 (2014). (doi, arXiv)

2013: Pseudo-Riemannian spectral triples and the harmonic oscillator (with Mario Paschke and Adam Rennie). Journal of Geometry and Physics 73, 37-55 (2013). (doi, arXiv)

2013: Electrodynamics from Noncommutative Geometry (with Walter D. van Suijlekom). Journal of Noncommutative Geometry 7, 433-456 (2013). (doi , arXiv)

2012: Particle Physics from Almost-Commutative Spacetimes (with Walter D. van Suijlekom). Reviews in Mathematical Physics 24, 1230004 (2012). (doi , arXiv)

Theses

2025: Aspects of Unbounded KK-theory, Habilitationsschrift, Rheinische Friedrich-Wilhelms-Universität Bonn.

2015: Lorentzian geometry and physics in Kasparov's theory (link), Ph.D. thesis in Mathematical Sciences, The Australian National University (supervisor: Adam Rennie).

2011: The Structure of Gauge Theories in Almost Commutative Geometries, Master's thesis in Physics & Astronomy, Radboud University Nijmegen (supervisor: Walter D. van Suijlekom).

NSeaG2023

I have organised the NSeaG2023 meeting, which took place at the Hausdorff Center for Mathematics (HCM) in Bonn in May 2023, and consisted of:

• a Hausdorff School on "Noncommutative Geometry and Operator Algebras", 2-5 May (Website);
• the NSeaG2023 Workshop, 8-12 May (Website).

The NSeaG2023 meeting was part of the series NSeaG — Noncommutative Geometry along the North Sea (see here or here).