Dr. Koen van den Dungen

I have recently organised the NSeaG2023 meeting, which took place at the Hausdorff Center for Mathematics (HCM) in Bonn in May 2023. It is part of the series NSeaG — Noncommutative Geometry along the North Sea — and consists of:
  • a Hausdorff School on "Noncommutative Geometry and Operator Algebras", 2-5 May (Website);
  • the NSeaG2023 Workshop, 8-12 May (Website).

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 2024-2025:
  • Graduate Seminar on Global Analysis (with Matthias Lesch): Dirac Operators and Spin Geometry.
    Preliminary meeting: Tuesday, 09 July 2024, 16:00, room 0.006, Endenicher Allee 60.
    As long as talks are available, late registrations are welcome via email to Prof. Lesch.
Summer semester 2024:
  • S1G1 Seminar: Geometrie & Analysis – Ausgewählte Beweise.
  • Assistent V2B3 Einführung in die Komplexe Analysis
See also my Past Teaching.

(See also: ORCID iD iconORCID, SCOPUS, arXiv, Google Scholar.)
2024: Dirac-Schrödinger operators, index theory, and spectral flow. arXiv:2407.02993
2023: Generalised Dirac-Schrödinger operators and the Callias Theorem. arXiv:2312.17600
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)

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 (link), Master's thesis in Physics & Astronomy, Radboud University Nijmegen (supervisor: Walter D. van Suijlekom).

Contact: kdungen@uni-bonn.de
Office: Room 1.032, Mathematical Institute (Endenicher Allee 60)