My current research interests are:

- Noncommutative geometry and operator systems
- Noncommutative geometry and quantum gauge fields
- Unbounded KK-theory: factorization of Dirac operators

#### Visitors

- Adam Rennie (Australian National University), July 2012
- Koen van den Dungen (Australian National University), July 2012
- Simon Brain (University of Luxembourg), June-December 2010
- Michael Borinsky (Humboldt Universat zu Berlin), November 2013-January 2014
- Matthias Sars (Humboldt Universat zu Berlin), March 2014
- Agostino Devastato (University of Napels), April-June 2014
- Iain Forsyth (Australian National University), June-December 2014
- Adam Rennie (Wollongong University), November 2015
- John Barrett (Nottingham University), January 2016
- Mairi Sakellariadou (King’s College), April 2016
- Koen van den Dungen (SISSA, Trieste), November-December 2017
- Ali Chamseddine (American University of Beireut), July-August 2018

#### Postdoctoral fellows

- Simon Brain, December 2013-November 2016
- Jord Boeijink, October-December 2014, currently working at Sioux LIME
- Jens Kaad, January 2015-January 2016, currently
*Associate Professor*, University of Southern Denmark. - Francesca Arici, October 2015-October 2018, currently
*Assistant Professor*, Leiden University. - Tyrone Crisp, January 2017-August 2018, currently
*Assistant Professor*, University of Maine. - Bram Mesland, April-August 2019, currently
*Assistant Professor*, Leiden University - Rui Dong, September 2019-November 2021
- Michael Florian Wondrak, June 2021- May 2024

#### Ph.D. Students

- Thijs van den Broek, Supersymmetry and the spectral action: On a geometrical interpretation of the MSSM (Ph.D., 2014), currently working at Andersson Elffers Felix
- Jord Boeijink, Dirac operators, gauge systems and quantisation (Ph.D., 2014), currently working at Sioux LIME
- Roberta Anna Iseppi, The BV Formalism for Matrix Models: A Noncommutative Geometric Approach (Ph.D., 2015), postdoc in Toronto
- Ruben Stienstra, Quantisation versus lattice gauge theory (Ph.D., 2019)
- Abel Stern, Finite approximation and continuous change in spectral geometry (Ph.D., 2021), currently working at Schuttelaar & Partners
- Teun van Nuland, C*-algebraic results in the search for quantum gauge fields (Ph.D., 2022)
- Mick Gielen (2021-2022, currently PhD-student at Oxford University).
- Malte Leimbach
- Collin Joseph

#### Master Students

- Jord Boeijink, Noncommutative Geometry of Yang-Mills Fields (M.Sc., 2009)
- Thijs van den Broek, Supersymmetric Gauge Theories in Noncommutative Geometry: First Steps Towards the MSSM (M.Sc., 2009)
- Koen van den Dungen, The structure of gauge theory in almost commutative geometries (M.Sc., 2011)
- Matthias Sars, Noncommutative geometry and SU(5) grand unification (M.Sc., 2011)
- Jins de Jong, Hybrid renormalization and the beta-functions of the real scalar Higgs Lagrangians from the scalar spectral action (M.Sc., 2013)
- Bas Jordans, Real dimensional spaces in noncommutative geometry (M.Sc., 2013)
- Dorianne van Dijk, An invariant of finite noncommutative geometric spaces (M.Sc., 2016)
- Laura Hesp, The perturbation semigroup of C*-algebras (M.Sc., 2016)
- Dennis Hendrikx (with Jens Kaad), The unbounded Kasparov module of a vertical Dirac operator (M.Sc., 2016)
- Fokke de Haan, Gauge theories on the circle (M.Sc., 2018)
- Luuk Verhoeven, Embedding the circle into the plane in unbounded KK-theory (M.Sc., 2019)
- Tey Berendschot, Truncated geometry (M.Sc., 2019)
- Jeroen Winkel, Connections and the fundamental group of non-commutative spaces

(M.Sc., 2019) - Yari Kraak, Fermionic particle creation in asymptotically static Generalized Friedmann–Lemaitre–Robertson–Walker spacetimes (M.Sc., 2021)
- Eva-Maria Hekkelman, Truncated geometry on the circle (M.Sc., 2021)
- Ian Koot, Properties of the propagation number (M.Sc., 2021)
- Friso van Dijk, Cyclic Cocycles in the Spectral Action on Manifolds (M.Sc., 2023)

#### Bachelor Students

- Richard Sanders, Graph C*-algebras (B.Sc., 2008)
- Moniek Verschuren, Coherent states in quantum mechanics (B.Sc., 2011)
- Nick Lubbers, Classificatie van eindige spectrale tripels (B.Sc., 2013)
- Stijn Marsman, Het Generalized Interval System (GIS) gegeneraliseerd – Een poging met groepoiden (B.Sc., 2013)
- Sue Brouns, Hilbert’s Derde Probleem (B.Sc., 2013)
- Dorianne van Dijk, Afbeeldingen tussen matrixalgebra’s (B.Sc., 2013)
- Niels Neumann (Honours Program), Perturbation semigroup for matrix algebras (B.Sc., 2014)
- Luuk Verhoeven (Honours Program), Can one hear the shape of a drum (B.Sc., 2015)
- Berend Visser, Matrix-groepen en hun representaties (B.Sc., 2015)
- Teun van Nuland, The perturbation semigroup of the noncommutative torus (B.Sc., 2016)
- Arne Jans
- Oscar de Wit, Group actions, critical points and critical fields (B.Sc., 2020)
- Suzan van Lingen, Relating division algebras to Hopf fibrations using K-theory (B.Sc., 2020)

#### Academic Background

From 1996 to 2001, I studied Theoretical Physics at the University of Amsterdam. My master’s thesis “Noncommutative geometry, deformation quantization and string theory” [pdf] was written under supervision of drs. G.G.A. Bauerle.

From September 2001 to August 2002, I followed a Program on Mathematical Physics at the Mathematics department of the University of Amsterdam. It consisted of the courses integration theory, analysis on manifolds, differential geometry and K-theory of C*-algebras. Besides these courses, I wrote a paper titled “The noncommutative cylinder and its K-theory” [pdf] under supervision of prof. dr. N.P. Landsman.

In September and October 2002, I was a guest-researcher at the Korteweg-de Vries Institute for Mathematics of the University of Amsterdam. My supervisor was prof. dr. N.P. Landsman and this position is part of the Pionier Project: “Quantization, noncommutative geometry and symmetry”. The research continued on the subjects of my physics thesis and mathematics paper and resulted in an article entitled “The noncommutative Lorentzian cylinder as an isospectral deformation”.

From November 2002 until November 2005, I was a PhD-student at the Mathematical Physics sector of SISSA in Trieste, Italy. My supervisors were Prof. Dabrowski (SISSA) and Prof. Landi(Universita’ di Trieste). The resulting PhD thesis: “Geometry of Noncommutative Spheres and their Symmetries”

From November 2005 until December 2006, I was a postdoc at the Max Planck Institute for Mathematics in Bonn where I worked on quantum gauge theories in the setting of the Connes-Kreimer Hopf algebra of Feynman graphs.

From January 2007-2009 I worked as a postdoc at the Institute for Mathematics, Astrophysics and Particle Physics at the Radboud University Nijmegen working in the group of prof. dr. N.P. Landsman.

From 2009-2011 I have worked on VENI-project “Noncommutative geometry of quantum gauge fields” and from 2012-2015 I was Assistant Professor at Radboud University Nijmegen.

In 2013 I have started my VIDI-project “Noncommutative geometry and quantum lattice gauge fields” and from 2015-2021 I was Associate Professor at Radboud University Nijmegen.

Since December 2021 I have been appointed Full Professor of “Noncommutative Geometry” at Radboud University Nijmegen.

#### Editorial work

Editor-in-chief of Mathematical Physics, Analysis and Geometry (section Quantum Theory)

Editor of Indagationes Mathematicae

Editor of Journal of Noncommutative Geometry

Editor of Journal of Functional Analysis