Preprints

• Convergence of spectral truncations for compact metric groups (with Yvann Gaudillot-Estrada)  

Publications

Noncommutative geometry and particle-physics

• Gravitational Pair Production and Black Hole Evaporation (with Michael Wondrak and Heino Falcke). Phys. Rev. Lett. 130, 221502   
• One-loop corrections to the spectral action (with Teun van Nuland). JHEP 078 (2022)  
• Cyclic cocycles in the spectral action (with Teun van Nuland). To appear in J. Noncomm. Geom.  
• Second quantization and the spectral action (with Rui Dong and Masoud Khalkhali). J. Geom. Phys. 167 (2021) 104285.  
• Spectral action in matrix form (with Ali H. Chamseddine and John Iliopoulos). Eur. Phys. J. C (2020) 80:1045.  
• Entropy and the spectral action (with Ali Chamseddine and Alain Connes). Commun. Math. Phys. 373 (2020) 457-471  
• Grand Unification in the Spectral Pati-Salam Model (with Ali Chamseddine and Alain Connes). JHEP11(2015)011  
• Beyond the Spectral Standard Model: Emergence of Pati-Salam Unification (with Ali Chamseddine and Alain Connes). JHEP 11 (2013) 132  
• Gauge networks in noncommutative geometry (with Matilde Marcolli). J. Geom. Phys. 75 (2014) 71-91  
• Inner Fluctuations in Noncommutative Geometry without the first order condition (with Ali Chamseddine and Alain Connes). J. Geom. Phys. 73 (2013) 222-234  
• Going beyond the Standard Model with noncommutative geometry (with Thijs van den Broek). JHEP 3 (2013) 112  
• Particle Physics from Almost Commutative Spacetimes (with Koen van den Dungen). Rev. Math. Phys. 24 (2012) 1230004  
• Supersymmetric QCD from noncommutative geometry (with Thijs van den Broek). Phys. Lett. B. 699 (2011) 119-122  
• Electrodynamics from Noncommutative Geometry (with Koen van den Dungen). J. Noncomm. Geom. 7 (2013) 433-456  
• The noncommutative geometry of Yang-Mills fields (with Jord Boeijink). J. Geom. Phys. 61 (2011) 1122-1134  
• Supersymmetric QCD and noncommutative geometry (with Thijs van den Broek). Commun. Math. Phys. 303 (2011) 149-173  

Noncommutative geometry and applications

• Gromov-Hausdorff convergence of spectral truncations for low-dimensional tori (with Malte Leimbach). To appear in Adv. Math.  
• Riemannian embeddings in codimension one as unbounded KK-cycles (with Luuk Verhoeven). Ann. K-theory 8 (2023) 645-668.  
• Operator systems for tolerance relations on finite sets (with Mick Gielen). Indag. Math. (available online)  
• Tolerance relations and operator systems (with Alain Connes). Acta Sci. Math.  
• Schatten classes for Hilbert modules over commutative C*-algebras (with Abel Stern). J. Funct. Anal. 281 (2021) 109042  
• Gromov-Hausdorff convergence of state spaces for spectral truncations. J. Geom. Phys. 162 (2021) 104075  
• Spectral truncations in noncommutative geometry and operator systems (with Alain Connes). Commun. Math. Phys. 383 (2021) 2021–2067.  
• Immersions and the unbounded Kasparov product: embedding spheres into Euclidean space (with Luuk Verhoeven). J. Noncommut. Geom. 16 (2022) 489-511.  
• Curvature of differentiable Hilbert modules and Kasparov modules (with Bram Mesland and Adam Rennie). Adv. Math. 402 (2022) 108128  
• The fundamental group of a noncommutative space (with Jeroen Winkel). Algebr. Represent. Theory 25 (2022) 1003-1035.  
• Factorization of Dirac operators on toric noncommutative manifolds (with Jens Kaad). J. Geom. Phys. 132 (2018) 282-300.  
• Reflection positivity in higher derivative scalar theories (with Francesca Arici, Daniel Becker, Chris Ripken, Frank Saueressig). J. Math. Phys. 59 (2018) 083202  
• Factorization of Dirac operators on almost-regular fibrations of spin$^c$ manifolds (with Jens Kaad). Documenta Math. 5 (2020) 2049–2084  
• On a theorem of Kucerovsky for half-closed chains (with Jens Kaad). J. Operator Theory 82 (2019) 115-145.  
• Reduction of quantum systems and the local Gauss law (with Ruben Stienstra). Lett. Math. Phys. 108 (2018) 2515-2522.  
• Quantum lattice gauge fields and groupoid C*-algebras (with Francesca Arici and Ruben Stienstra). Annales Henri Poincare 19 (2018) 3241-3266.  
• Noncommutative geometry and the BV formalism: application to a matrix model (with Roberta Iseppi). J. Geom. Phys 120 (2017) 129-141.  
• Riemannian submersions and factorization of Dirac operators (with Jens Kaad). J. Noncommut. Geom. 12 (2018) 1133-1159.  
• Quantization commutes with singular reduction: cotangent bundles of compact Lie groups (with Jord Boeijink and Klaas Landsman). Rev. Math. Phys. 31 (2019) 1950016  
• Localizing gauge theories from noncommutative geometry. Adv. Math. 290 (2016) 682-708.  
• Perturbation semigroup of matrix algebras (with Niels Neumann). J. Noncomm. Geom 10 (2016) 245-264  
• Gauge Theory for Spectral Triples and the Unbounded Kasparov Product (with Simon Brain and Bram Mesland). J. Noncomm. Geom. 10 (2016) 135-206  
• Perturbations and operator trace functions. Journ. Funct. Anal. 260 (2011) 2483-2496  
• Holomorphic structures on the quantum projective line (with G. Landi and M. Khalkhali). Int. Math. Res. Not. IMRN (2010) doi 10.1093/imrn/rnq097  
• Noncommutative tori and the Riemann-Hilbert correspondence (with S. Mahanta). J. Noncomm. Geom. 3 (2009) 261-287  
• The Dirac operator on SUq(2) (with L. Dabrowski, G. Landi, A. Sitarz and J. Varilly). Commun. Math. Phys. 259 (2005), 729-759  
• The local index formula for SUq(2) (with L. Dabrowski, G. Landi, A. Sitarz and J. Varilly). K-Theory 35 (2005) 375-394  
• The noncommutative Lorentzian cylinder as an isospectral deformation. J. Math. Phys. 30 (2004), 537-556  

Noncommutative geometry and renormalization

• Renormalizability conditions for almost-commutative manifolds. Annales Henri Poincare 15 (2014), 985-1011  
• Renormalizability conditions for almost-commutative geometries. Phys. Lett. B711 (2012) 434-438  
• Renormalization of the asymptotically expanded Yang-Mills spectral action. Commun. Math. Phys. 312 (2012) 883-912  
• Renormalization of the spectral action for the Yang-Mills system. JHEP 3 (2011) 146  

Renormalization of gauge theories using Hopf algebras

• Quantization of gauge fields, graph polynomials and graph cohomology (with Dirk Kreimer and Matthias Sars). Annals of Physics 336 (2013) 180-222  
• The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras. Commun. Math. Phys. 290 (2009) 291-319  
• Recursive relations in the core Hopf algebra (with D. Kreimer). Nucl. Phys. B820 (2009) 682-693  
• Renormalization of gauge fields: A Hopf algebra approach. Commun. Math. Phys. 276 (2007) 773-798  
• The Hopf algebra of Feynman graphs in QED. Lett. Math. Phys. 77 (2006) 265-281  

Instantons on toric noncommutative manifolds

• Moduli Spaces of Instantons on Toric Noncommutative Manifolds (with Simon Brain, Giovanni Landi). Adv. Theor. Math. Phys. 17 (2013) 1129 – 1193.  
• The ADHM Construction of Instantons on Noncommutative Spaces (with Simon Brain). Rev. Math. Phys. 23 (2011) 1-47  
• Noncommutative families of instantons (with G. Landi, C. Pagani and C. Reina). Int. Math. Res. Not. IMRN 12 Art. ID rnn038 (2008)  
• Noncommutative instantons from twisted conformal symmetries (with G. Landi). Commun. Math. Phys. 271 (2007) 591-634  
• Principal fibrations from noncommutative spheres (with G. Landi). Commun. Math. Phys. 260 (2005), 203-225  

Conference proceedings

• Cyclic cocycles and one-loop corrections in the spectral action (with Teun D.H. van Nuland). In "Cyclic cohomology at 40". Achievements and Future Prospects. (Eds. A. Connes, C. Consani, B.I. Dundas, M. Khalkhali, H. Moscovici) Proceedings of Symposia in Pure Mathematics 105 (2023) 513-533.  
• Noncommutativity and Physics: A non-technical review (with Ali Chamseddine and Alain Connes). Eur. Phys. J. Spec. Top. (2023)  
• A survey of spectral models of gravity coupled to matter (with A. Chamseddine). In Advances in Noncommutative Geometry. Eds. A. Chamseddine, C. Consani, N. Higson, M. Khalkhali, M. Moscovici and G. Yu. Springer, 2020.  
• Higher-derivative gauge theories from noncommutative geometry. PoS Corfu 2011  
• The Hopf algebraic structure of perturbative quantum gauge theories. In Noncommutative Geometry, Arithmetic, and Related Topics, Eds. C. Consani and A. Connes. Johns Hopkins University Press, 2011  
• Combinatorics and Feynman graphs for gauge theories. In Combinatorics and Physics. Eds. K. Ebrahimi-Fard, M. Marcolli and W. van Suijlekom. Cont. Math. 539 (2011) 417-442  
• In Motives, QFT and PsiDOs conference, Eds. A. Carey, D. Ellwood, S. Paycha and S. Rosenberg. Clay Mathematics Proceedings 12, 2011.  
• Renormalization Hopf algebras for gauge symmetries and BRST-symmetries. In Motives, QFT and PsiDOs conference, Eds. A. Carey, D. Ellwood, S. Paycha and S. Rosenberg. Clay Mathematics Proceedings 12, 2011  
• Renormalization of gauge fields using Hopf algebras. In Quantum Field Theory, Eds. B. Fauser, J. Tolksdorf and E. Zeidler, Birkhauser Verlag, Basel, 2008  
• Multiplicative renormalization and Hopf algebras. In Arithmetic and geometry around quantization. Eds. O. Ceyhan, Yu.-I. Manin and M. Marcolli. Progress in Mathematics 279, Birkhauser Verlag, Basel, 2010  
• Noncommutative Bundles and Instantons in Tehran (with G. Landi). In An Invitation to Noncommutative Geometry, Eds. M. Khalkhali and M. Marcolli, World Scientific Publishing, Hackensack, 2008  
• The noncommutative spin geometry of quantum SU(2), Comptes-Rendus des Rencontres Mathematiques de Glanon, 2005.  

Theses

• Geometry of Noncommutative Spheres and their Symmetries, Ph.D. Thesis, SISSA, 2005  
• Noncommutative geometry, deformation quantization and string theory, M.Sc. Thesis, UvA, 2001  

Books

• A survey of spectral models of gravity coupled to matter (with A. Chamseddine). Book chapter in Advances in Noncommutative Geometry (A. Chamseddine, C. Consani, N. Higson, M. Khalkhali, H. Moscovici, G.Yu (Eds.)). Springer 2019.   
• Symmetrie in de deeltjesfysica. Epsilon Uitgaven, 2016.   
• Supersymmetry and Noncommutative Geometry (with Wim Beenakker and Thijs van den Broek). SpringerBrief in Mathematical Physics 9, Springer, 2016.  
• Noncommutative Geometry and Particle Physics, Mathematical Physics Studies, Springer 2015. List of Errata to first edition draft version (Book review by Matilde Marcolli in Bulletin of the AMS   
• Combinatorics and Physics. Eds. K. Ebrahimi-Fard, M. Marcolli and W. van Suijlekom. Cont. Math. 539 (2011).  

Popular

• Oratie: Opgetrommeld voor spectra in de meetkunde. Nieuw Archief voor Wiskunde 5/23 nr. 4 (december 2022) 208-217  
• The spectral model of particle physics. Nieuw Archief voor Wiskunde 5/15 nr.4 (december 2014) 240-250   
• Ricci-stroming in 2D (met E. van Dongen en J. Vervoort), Nieuw Archief voor Wiskunde 5/12 (september 2011) 212-216   
• Interview Alain Connes. The flashes of insight never came for free (with G. Cornelissen and N.P. Landsman), Nieuw Archief voor Wiskunde 5/11 (december 2010) 250-256  
• Niet-commutatieve meetkunde niet-communicabel? (in dutch), Nieuw Archief voor Wiskunde 5/7 (maart 2006) 27-31  

Other

• Article review "Geometry and the quantum: basics" by Chamseddine, Connes and Mukhanov (JHEP 2014, 098), Mathematical Reviews, AMS.   
• Book review Alain Connes, Matilde Marcolli: "Noncommutative geometry, quantum fields and motives". Mathematical Reviews, AMS.  
• Book review Frederic Paugam: “Towards the Mathematics of Quantum Field Theory” To appear in Jahresber Dtsch Math-Ver.   
• Combinatorics and Feynman graphs for gauge theories, lecture notes  
• Noncommutative Geometry and Particle Physics, short survey