• Functional Analysis (measures on topological spaces, operator algebras, ...)
  • Differential Geometry (stratifications, diffeomorphisms, ...)
  • Mathematical Physics (quantum geometry, quantum gravity, ...)
  • Quantization (loop quantization vs symmetry reduction, ...)


  1. Eva-Maria Engelen, Christian Fleischhack, Giovanni Galizia, Katharina Landfester (Hrsg.): Heureka – Evidenzkriterien in den Wissenschaften. Ein Kompendium für den interdisziplinären Gebrauch. Spektrum Akademischer Verlag, 2010.

Preprints of most of my articles may also be obtained via or via the MPI preprint server, reviews via MathSciNet (provided you have access to it)

  1. Continuity of States on Non-Unital Differential Algebras in Loop Quantum Cosmology. Commun. Math. Phys. 370 (2019) 531–539.
  2. Spectra of Abelian C*-Subalgebra Sums. Vietnam J. Math. 47 (2019) 195–208. 
  3. Loop Quantization and Symmetry: Configuration Spaces. Commun. Math. Phys. 360 (2018) 481–521.
  4. Kinematical Foundations of Loop Quantum Cosmology. 
    In: Quantum Mathematical Physics: A Bridge between Mathematics and Physics (Edited Volume, Birkhäuser, Basel, 2016), pp. 201–232. 
  5. (with Philipp Levermann)  Ashtekar Variables: Structures in Bundles. Vietnam J. Math. 44 (2016) 203–214.
  6. Symmetries of Analytic Paths. 1503.06341 [math-ph] (74 pp.)
  7. (with Johannes Brunnemann)  Non-Almost Periodicity of Parallel Transports for Homogeneous Connections. Math. Phys. Anal. Geom. 15 (2012) 299–315.
  8. On Ashtekar's Formulation of General Relativity. J. Phys. (Conf. Ser.) 360 (2012) 012022. (10 pp.)
  9. (with Shmuel Friedland)  Asymptotic Positivity of Hurwitz Product Traces: Two Proofs. Lin. Alg. Appl. 432 (2010) 1363–1383.
  10. Representations of the Weyl Algebra in Quantum Geometry. Commun. Math. Phys. 285 (2009) 67–140.
  11. Kinematical Uniqueness of Loop Quantum Gravity. 
    In: Quantum Gravity: Mathematical Models and Experimental Bounds (Edited Volume, Birkhäuser, Basel, 2007), pp. 203–219. 
  12. Irreducibility of the Weyl Algebra in Loop Quantum Gravity. Phys. Rev. Lett. 97 (2006) 061302. (4 pp.) 
  13. Quantization Restrictions for Diffeomorphism Invariant Gauge Theories. 
    In: Quantization and Analysis on Symmetric Spaces (Proceedings, Wien, 2006), pp. 55–63.
  14. Construction of Generalized Connections. math-ph/0601005 (12 pp.)
  15. Proof of a Conjecture by Lewandowski and Thiemann. Commun. Math. Phys. 249 (2004) 331–352.
  16. Parallel Transports in Webs. Math. Nachr. 263–264 (2004) 83–102.
  17. Regular Connections among Generalized Connections. J. Geom. Phys. 47 (2003) 469–483.
  18. On the Gribov Problem for Generalized Connections. Commun. Math. Phys. 234 (2003) 423–454.
  19. Hyphs and the Ashtekar-Lewandowski Measure. J. Geom. Phys. 45 (2003) 231–251.
  20. (with Jerzy Lewandowski)  Breakdown of the Action Method in Gauge Theories. math-ph/0111001 (4 pp.) (extension of my paper math-ph/0107022 without co-author)
  21. On the Support of Physical Measures in Gauge Theories. math-ph/0109030 (42 pp.)
  22. Stratification of the Generalized Gauge Orbit Space. Commun. Math. Phys. 214 (2000) 607–649.
  23. A new type of loop independence and SU(N) quantum Yang-Mills theory in two dimensions. J. Math. Phys. 41 (2000) 76–102.
  1. (with Miloš Vec)
    Vom Nutzen und Nachteil digitaler Geräte in der Vorlesung.
    In: Perspektiven wechseln 2020 (Akkermann, Kanske [Hrsg.], Jan Thorbecke, 2019) – Kalender der Jungen Akademie.
  2. (with Eva-Maria Engelen, C. Giovanni Galizia, Katharina Landfester)
    Heureka – Oder: Wann jubeln Wissenschaftler? Evidenzgewinnung und -erzeugung im Forschungsalltag. 
    In: Forschung und Lehre 17 (2010) 810–812.   Nachdruck auf
  3. Mathematik ist eine Glaubensfrage. 
    In: Heureka – Evidenzkriterien in den Wissenschaften (Engelen et al. [Hrsg.], Spektrum, 2010), pp. 150–168.
  4. Oberwolfach: Der Welt entrückt im Paradies der Mathematiker. 
    In: Mekkas der Moderne (Schmundt et al. [Hrsg.], Böhlau, 2010).   Nachdruck in: sciencegarden – Magazin für junge Forschung, 2010.
  5. Quantengravitation: Keine Experimente, aber Mathematik. 
    In: Jahrbuch der Max-Planck-Gesellschaft für 2006 (Max-Planck-Gesellschaft [Hrsg.], 2006).
  1. (with Matilde Marcolli, Ryszard Nest)  Noncommutative Geometry and Loop Quantum Gravity: Loops, Algebras and Spectral Triples. Introduction by the Organisers. Oberwolfach Rep. 7 (2010) 373--375.
  1. Judith R. Goodstein: Einstein's Italian Mathematicians – Ricci, Levi-Civita, and the Birth of General Relativity (AMS, 2018).
    In: Math. Semesterber. (2021, accepted). (in German)
  2. Titu Andreescu and Branislav Kisačanin: Math Leads for Mathletes 1 & 2 – A rich resource for young math enthusiasts, parents, teachers, and mentors (XYZ Press, LLC. 2014, 2018).
    In: Math. Semesterber. 67  (2020) 103–107. (in German)
  3. Neue Bücher aus Oberwolfach. 
    In: Mitteilungen der DMV 18 (2010) 11.


Mathematische und physikalische Aspekte verallgemeinerter Eichfeldtheorien im Ashtekarprogramm. Leipzig, 2001.

Diploma Thesis (Mathematics)

Stratifizierung des verallgemeinerten Eichorbitraums im Ashtekarprogramm. Leipzig, 1999.

Diploma Thesis (Physics)

Funktionalintegralzugang zu Eichtheorien und Gravitation im Rahmen des Ashtekarprogramms. Leipzig, 1998.


The Emmy-Noether program of the Deutsche Forschungsgemeinschaft provided me with full funding of an independent junior research group. Details may be found here.


These workshops take place in Tux (Austria) each February. Since 2016, the team of organizers consists of Norbert Bodendorfer, Jerzy Lewandowski, Hanno Sahlmann and myself. The workshops' focus is on loop quantum gravity and related areas.

LQP workshops usually take place once per semester at varying institutions, mostly in northern Germany. Originally, they have been called "Workshops on Foundations and Constructive Aspects of Quantum Field Theory", now they have been well-known under the LQP label where LQP stands for "local quantum physics".

  • LQP 45 (Paderborn, June 2020) – cancelled due to Covid-19 pandemic
  • LQP 30 (Paderborn, June 2012)

Oberwolfach Workshop "Loops, Algebras, and Spectral Triples'' (Oberwolfach, February 2010)  co-organizers: Matilde Marcolli and Ryszard Nest

Beyond the events above, I have co-organised several other conventions:

  • GDMV 2018 Conference (Paderborn, March 2018) as a member of the Team of Organizers
  • Loops '17 Conference (Warszawa, July 2017)  as a member of the Scientific Organising Committee
  • Loops '15 Conference (Erlangen, July 2015)  as a member of the International Organising Committee
  • 2nd British-German Frontiers-of-Science Symposion (Potsdam, May 2008)  Royal Society, Humboldt-Stiftung, Junge Akademie
  • Workshop "Frontiers of Quantum Theory: Reality and Randomness'' (Berlin, April 2008)  Junge Akademie
  • 1st British-German Frontiers-of-Science Symposion (Wyboston, March/April 2006)  Royal Society, Humboldt-Stiftung, Junge Akademie