Dr. Koen van den Dungen

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.

Teaching
Wintersemester 2018-2019:
  • Graduate Seminar on Global Analysis: Introduction to C*-algebras: Overview

Publications
(See also: ORCID, SCOPUS, arXiv.)
2018: Locally bounded perturbations and (odd) unbounded KK-theory. To appear in Journal of Noncommutative Geometry. (arXiv)
2018: The index of generalised Dirac-Schrödinger operators. To appear in Journal of Spectral Theory. (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)

Preprints
2018: The Kasparov product on submersions of open manifolds. (arXiv:1811.07824)
2018: Addendum to: Indefinite Kasparov modules and pseudo-Riemannian manifolds. (arXiv:1807.11856)
2018: A perspective from (unbounded) KK-theory. Appendix to: The spectral flow of a family of Toeplitz operators (by Maxim Braverman). (arXiv:1803.11101)

Theses
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