Christian Fleischhack

Universität Paderborn
Institut für Mathematik
Warburger Str. 100
33098 Paderborn

Office:
D1.201
Phone:
+49 5251 60-2628
Fax:
+49 5251 60-3836
E-mail:
christian.fleischhack[at]math.uni-paderborn.de

Hint for students: When sending me e-mails, please use your university e-mail address. For data privacy reasons, I reserve for myself the right to ignore any study-related e-mail sent from an account outside the university.

Teaching

In this term, I am teaching Analysis 1 (in German).

For teaching in previous terms, please click here.

Research

Interests

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

Funding

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

Workshops

  • Fourth Tux Workshop on Quantum Gravity (Tux, February 2016) co-organizers: Norbert Bodendorfer, Jerzy Lewandowski, Hanno Sahlmann
  • Loops '15 Conference (Erlangen, July 2015) as a member of the International Organising Committee
  • 30th Workshop "Foundations and Constructive Aspects of Quantum Field Theory'' (Paderborn, June 2012)
  • Oberwolfach Workshop "Loops, Algebras, and Spectral Triples'' (Oberwolfach, February 2010) co-organizers: Matilde Marcolli and Ryszard Nest
  • 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

Publications

Books

  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.

Research Articles

Preprints of most of my articles may also be obtained via arXiv.org or via the MPI preprint server, reviews via MathSciNet (provided you have access to it)
  1. Loop Quantization and Symmetry: Configuration Spaces. Commun. Math. Phys. (to appear), 43 pp.
  2. Kinematical Foundations of Loop Quantum Cosmology.
    In: Quantum Mathematical Physics: A Bridge between Mathematics and Physics (Edited Volume, Birkhäuser, Basel, 2016), pp. 201–232.
  3. (with Philipp Levermann)  Ashtekar Variables: Structures in Bundles. Vietnam J. Math. 44 (2016) 203–214.
  4. Symmetries of Analytic Paths. 1503.06341 [math-ph] (74 pp.)
  5. Spectra of Abelian C*-Subalgebra Sums. 1409.5273 [math.FA] (12 pp.)
  6. (with Johannes Brunnemann)  Non-Almost Periodicity of Parallel Transports for Homogeneous Connections. Math. Phys. Anal. Geom. 15 (2012) 299–315.
  7. On Ashtekar's Formulation of General Relativity. J. Phys. (Conf. Ser.) 360 (2012) 012022. (10 pp.)
  8. (with Shmuel Friedland)  Asymptotic Positivity of Hurwitz Product Traces: Two Proofs. Lin. Alg. Appl. 432 (2010) 1363–1383.
  9. Representations of the Weyl Algebra in Quantum Geometry. Commun. Math. Phys. 285 (2009) 67–140.
  10. Kinematical Uniqueness of Loop Quantum Gravity.
    In: Quantum Gravity: Mathematical Models and Experimental Bounds (Edited Volume, Birkhäuser, Basel, 2007), pp. 203–219.
  11. Irreducibility of the Weyl Algebra in Loop Quantum Gravity. Phys. Rev. Lett. 97 (2006) 061302. (4 pp.)
  12. Quantization Restrictions for Diffeomorphism Invariant Gauge Theories.
    In: Quantization and Analysis on Symmetric Spaces (Proceedings, Wien, 2006), pp. 55–63.
  13. Construction of Generalized Connections. math-ph/0601005 (12 pp.)
  14. Proof of a Conjecture by Lewandowski and Thiemann. Commun. Math. Phys. 249 (2004) 331–352.
  15. Parallel Transports in Webs. Math. Nachr. 263–264 (2004) 83–102.
  16. Regular Connections among Generalized Connections. J. Geom. Phys. 47 (2003) 469–483.
  17. On the Gribov Problem for Generalized Connections. Commun. Math. Phys. 234 (2003) 423–454.
  18. Hyphs and the Ashtekar-Lewandowski Measure. J. Geom. Phys. 45 (2003) 231–251.
  19. (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)
  20. On the Support of Physical Measures in Gauge Theories. math-ph/0109030 (42 pp.)
  21. Stratification of the Generalized Gauge Orbit Space. Commun. Math. Phys. 214 (2000) 607–649.
  22. A new type of loop independence and SU(N) quantum Yang-Mills theory in two dimensions. J. Math. Phys. 41 (2000) 76–102.

Reports

  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.

General Articles

  1. (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 academics.de.
  2. Mathematik ist eine Glaubensfrage.
    In: Heureka – Evidenzkriterien in den Wissenschaften (Engelen et al. [Hrsg.], Spektrum, 2010), pp. 150–168.
  3. 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.
  4. Neue Bücher aus Oberwolfach.
    In: Mitteilungen der DMV 18 (2010) 11.
  5. Quantengravitation: Keine Experimente, aber Mathematik.
    In: Jahrbuch der Max-Planck-Gesellschaft für 2006 (Max-Planck-Gesellschaft [Hrsg.], 2006).

Theses (in German)

Dissertation
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.

Links

Institutions

Ressources

Further Information

Alumnus of the Young Academy

August 2006 – September 2009
Head of an Emmy Noether Independent Junior Research Group at the Mathematics Department of Hamburg University

April 1998 – July 2006 (partly on leave)
PhD student / Researcher at the Max-Planck Institute for Mathematics in the Sciences in Leipzig

October – November 2001 and May 2002 – May 2003
Visiting Research Scholar at the Center for Gravitational Physics and Geometry at Penn State University

Please note: I am NOT a member of any social network service apart from Daidalosnet, the alumni network of the Studienstiftung. So if you find a person named Christian Fleischhack at platforms like facebook, stayfriends, etc.: That's NOT me!

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