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.
- Current Teaching
- Wintersemester 2022-23:
- Graduate Seminar on Global Analysis: K-theory of C*-algebras.
Overview
- Sommersemester 2022:
- Einführung in die Geometrie und Topologie.
- See also my Past Teaching.
- Graduate Seminar on Global Analysis: K-theory of C*-algebras.
- Publications
- (See also: ORCID, SCOPUS, arXiv, Google Scholar.)
- 2022: Localisations of half-closed modules and the unbounded Kasparov product. International Mathematics Research Notices, published online. (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)
- 2022: Localisations of half-closed modules and the unbounded Kasparov product. International Mathematics Research Notices, published online. (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).
- 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
Prof. Valentin Blomer und Prof. Georg Oberdieck erhalten ERC grants
Prof. Peter Scholze erhält Lehrpreis der Universität
Ausschreibung: W3-Professur Reine Mathematik
Bonn Mathematics ranked 15th in Shanghai Ranking
Prof. Carl-Friedrich Bödigheimer hat Daidalos-Münze der Studienstiftung erhalten
Grants for Mathematics students from Ukraine
Corona: Measures at the Center for Mathematics
Prof. Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society
Georg Oberdieck receives Dubrovin Medal 2022
Prof. Peter Scholze elected as Foreign Member of the Royal Society
Prof. Dr. Jessica Fintzen new at the Mathematical Institute
Otto Toeplitz memorial fund established
Hausdorff Memorial Prize 2020/2021 awarded
Bachelorpreis 2020/21 der BMG verliehen
Prof. Christoph Thiele is holding the Clay Lecture 2022
Hausdorff Edition „Felix Hausdorff - Gesammelte Werke“
Prof. Catharina Stroppel invited as plenary speaker to the ICM 2022 in St. Petersburg
Bonner Mathematik belegt bei Shanghai Ranking den 1. Platz in Deutschland und weltweit den 13. Platz
Prof. Georg Oberdieck erhält Heinz Maier-Leibnitz-Preise 2020
Prof. Daniel Huybrechts erhält gemeinsam mit Debarre, Macri und Voisin ERC Synergy Grant