Mathematical Work of Markus Pflaum

  Editorial Work
  Diploma, PhD and Habilitation Thesis
  Selected Talks


  Differentiable stratified groupoids and a de Rham Theorem for inertia spaces,
    joint with C. Farsi und Ch. Seaton, arXiv:1511.00371 (2015)

  Whitney functions determine the real homotopy type of a semi-analytic set,
    joint with B. Chriestenson, arXiv:1403.1627 (2014)

  The profinite dimensional manifold structure of formal solution spaces of formally integrable PDE's,
    joint with B. Güneysu, arXiv:1308.1005 (2013)


  The transverse index theorem for proper cocompact actions of Lie groupoids,
    joint with H. Posthuma and X. Tang, Journal of Differential Geometry 99, 443-472 (2015),
    arXiv version available at

  Stratifications of inertia spaces of compact Lie group actions,
    joint with C. Farsi und Ch. Seaton, Journal of Singularities, Vol. 13, 107-140 (2015),
    arXiv version available at arXiv:1207.0595

  Quantization of Whitney functions and reduction,
    joint with H. Posthuma and X. Tang, Journal of Singularities, Vol. 13, 217-228 (2015),
    arXiv version available at arXiv:1310.6415

  The localized longitudinal index theorem for Lie groupoids and the van Est map,
    joint with H. Posthuma and X. Tang, Advances in Math. 270, 223-262 (2015),
    arXiv version available at arXiv:1112.4857

  The index of geometric operators on Lie groupoids,
    joint with H. Posthuma and X. Tang, Indagationes Mathematicae, Volume 25, Issue 5, 1135-1153 (2014),
    arXiv version available at arXiv:1308.0236

  Geometry of orbit spaces of proper Lie groupoids,
    joint with H. Posthuma and X. Tang, J. für die Reine und Angew. Math. 694, 49-84 (2014),
    arXiv version available at arXiv:1101.0180

  Quantization of Whitney functions,
    joint with H. Posthuma and X. Tang, Travaux mathématiques, Vol. XX 2012, 153-165 (2012),
    arXiv version available at arXiv:1202.5575

  Connes-Chern character for manifolds with boundary and eta cochains,
    joint with H. Moscovici and M. Lesch, Memoirs of the Amer. Math. Soc. Vol. 220, Nr. 1036 (2012),
    arXiv version available at arXiv:0912.0194

  Orbifold cup products and ring structures on Hochschild cohomologies
    joint with H. Posthuma and X. Tang, Communications in Contemporary Mathematics 13, 123-182 (2001)
    arXiv version available at arXiv:0706.0027

  Cyclic cocycles on deformation quantizations and higher index theorems
    joint with H. Posthuma and X. Tang, Advances in Math. 223, 1958-2021 (2010)
    arXiv version available at arXiv:0805.1411

  On the algebraic index for riemannian étale groupoids,
    joint with H. Posthuma and X. Tang, Lett. in Math. Physics 90, No. 1 - 3, 287-310 (2009)

  On the existence of star products on quotient spaces of linear Hamiltonian torus actions
    joint with H.-C. Herbig and S. Iyengar, Lett. in Math. Physics 89, No. 2, 101-113 (2009)
    arXiv version available at arXiv:0811.2152

  Relative pairing in cyclic cohomology and divisor flows
    joint with M. Lesch and H. Moscovici, Journal of K-Theory, Volume 3, Issue 02, 359-407 (2009)
    arXiv version available at arXiv:math/0603500

  From Weyl quantization to modern algebraic index theory,
    in Groups and Analysis: The Legacy of Hermann Weyl (Ed. Katrin Tent),
    London Mathematical Society Lecture Note Series No. 354,
    Cambridge University Press (2008)

  Regularized traces and K-theory invariants of parametric pseudodifferential operators,
    joint with M. Lesch and H. Moscovici,
    in Proceedings of the conference on Traces in Geometry, Number Theory and Quantum Fields
    held at the Max-Planck-Institute, Bonn, October 2005, Eds. S. Albeverio, M. Marcolli, S. Paycha and J. Plazas,
    Vieweg-Verlag, Wiesbaden (2008)

  On the homology of algebras of Whitney functions on subanalytic sets,
    joint with J.P. Brasselet, Annals of Math. 167, No. 1, 1-52 (2008)

  A homological approach to singular reduction in deformation quantization,
    joint with M. Bordemann and H.-C. Herbig,
    in Singularity Theory (Eds. Chéniot, dedicated to Jean-Paul Brasselet on his 60th birthday,
    Proceedings of the 2005 Marseille Singularity School and Conference CIRM, Marseille, France 24 January - 25 February 2005,
    World Scientific (2007)

  An algebraic index theorem for orbifolds,
    joint with H. Posthuma and X. Tang, Advances in Math. 210, 83-121 (2007)
    arXiv version available at arXiv:math/0507546

  Deformation Theory,
    Encyclopaedia in Mathematical Physics (Eds. J.-P. Francoise, G.L. Naber, and T.S. Tsou), Elsevier (2006)

  Homology of formal deformations of proper etale Lie groupoids,
    joint with N. Neumaier, H. Posthuma and X. Tang, Journal für die Reine und Angewandte Mathematik 593, 117-168 (2006)

  Phase Space Reduction of Star Products on Cotangent Bundles,
    joint with N. Kowalzig and N. Neumaier, Annales Henri Poincare 6, No. 3, 485-552 (2005)

  On the deformation quantization of symplectic orbispaces,
  Diff. Geometry and its Applications 19, 343-368 (2003)

  On representations of star product algebras over cotangent spaces on Hermitian line bundles
    joint with Martin Bordemann, Nikolai Neumaier and Stefan Waldmann, J. of Func. Analysis 199, 1-47 (2003)

  Analytic and Geometric Study of Stratified Spaces
    Lecture Notes in Mathematics, vol. 1768, Springer-Verlag (2001)

  Smooth structures on stratified spaces
    in Quantization of Singular Symplectic Quotients,
    Eds. N.P. Landsman, M. Pflaum, and M. Schlichenmaier,
    Progress in Mathematics, vol. 198, Birkhäuser-Verlag (2001), 231-258)

  Continuous Hochschild homology for algebras of smooth functions
    in Coherent States, Quantization and Gravity,
    Proceedings of the XVII Workshop on Geometric Methods in Physics, Bialowieza, Poland, July 1998,
    Eds. M. Schlichenmaier, A. Strasburger, S.T. Ali, and A. Odzijewicz,
    Wydawnictwa Uniwersytetu Warszawskiego (2001), 37-44)

  A deformation theoretical approach to normal order quantization
    Russ. J. Math. Physics 7, No. 1, 83-113 (2000)

  Traces on algebras of parameter dependent pseudodifferential operators and the eta-invariant
    joint with M. Lesch, Trans. Amer. Math. Soc. 352 (2000), no. 11, 4911-4936)

  Deformation quantization on cotangent bundles
    Reports on Mathematical Physics 43, 291-297 (1999)

  A deformation theoretical approach to Weyl quantization on Riemannian manifolds
    Lett. Math. Physics 45, 277-294 (1998)

  Holomorphic deformation of Hopf algebras and application to quantum groups
    joint with M. Schottenloher, Journal of Geometry and Physics 28, 31-44 (1998)

  The normal symbol on Riemannian manifolds
     New York Journal of Mathematics 4, 97-125 (1998)

  On continuous Hochschild homology and cohomology groups
    Lett. Math. Physics 44, 43-51 (1998)

  Differential calculi on noncommutative bundles
    joint with Peter Schauenburg, Z. Phys. C 76, 733-744 (1997)

  Quantum groups on fibre bundles
    Comm. Math. Physics 166, 279-315 (1994)


  Liber Mathematicae: a web-based documentation and collaboration project for mathematics
    joint with J. Tuley, in Mathematics journals: what is valued and what may change.
    Report of the workshop held at MSRI, Berkeley, California on February 14 - 16, 2011,
    extended version available at arXiv:1102.5720 (2011)

  Poisson geometry and applications
    Abstracts from the workshop held April 29-May 5, 2007.
    Organized by Anton Alekseev, Rui Loja Fernandes, Eckhard Meinrenken and Markus Pflaum.
    Oberwolfach Rep. 4, no. 2, 1243-1298 (2007)

Editorial Work

  Noncommutative Geometry and Global Analysis, Proceedings of a conference in honor of Henri Moscovici
    Edited by A. Connes, A. Gorokhovsky, M. Lesch, M.J. Pflaum, and B. Rangipour,
    Contemporary Mathematics 546, Amer. Math. Soc. (2011)

  Quantization of singular symplectic quotients
    Edited by N.P. Landsman, M. Pflaum and M. Schlichenmaier,
    Progress in Mathematics 198, Birkhäuser Verlag, Basel (2001)

Diploma, PhD and Habilitation Thesis

  Ein Beitrag zur Geometrie und Analysis auf stratifizierten Räumen
    Habilitation Thesis, Mathematisch-Naturwissenschaftlichen Fakultät II der Humboldt-Universität zu Berlin, April 2000

  Local Analysis of Deformation Quantization
    Dissertation, Universität München, August 1995

  Quantengruppen auf Faserbündeln
    Diploma Thesis, Sektion Physik, Universität München, November 1992

Selected Talks

  Habilitation Talk Gibt es in der Mathematik ein Pfadintegral?
    Humboldt Universität zu Berlin, 10. Januar 2001

  Cyclic homology of deformation quantizations over orbifolds
    talk at the CMS Winter 2006 Meeting, December 9-11, 2006

Markus Pflaum
Last modified: Sep 30 12:08:00 2015