Dr. Koen van den Dungen
- NSeaG2023
- 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.
Overview
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.
- Graduate Seminar on Global Analysis (with Matthias Lesch): Dirac Operators and Spin Geometry.
- Summer semester 2024:
- S1G1 Seminar: Geometrie & Analysis – Ausgewählte Beweise.
Overview
- Assistent V2B3 Einführung in die Komplexe Analysis
- S1G1 Seminar: Geometrie & Analysis – Ausgewählte Beweise.
- See also my Past Teaching.
- Publications
- (See also: ORCID, 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)
- 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
Office: Room 1.032, Mathematical Institute (Endenicher Allee 60)
News
EMS Prize 2024 for Jessica Fintzen
Bonn mathematics performs excellently again in QS ranking
Stefan Schwede is invited speaker at the ECM 2024 in Sevilla
Jessica Fintzen wins Cole Prize
Regula Krapf receives university teaching award
Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts
Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019
Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023
Grants for Mathematics students from Ukraine
Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society
Peter Scholze elected as Foreign Member of the Royal Society