Christian Blohmann
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Christian Blohmann
Department of Mathematics
University of California
Berkeley, CA 94720-3840
USA

Phone: +1 (510) 643-7857
Office: 703 Evans Hall
Office hours: Wednesday 11:00am - 12:00pm

Email: blohmann@math.berkeley.edu

Short CV

I have studied Physics and Mathematics in Konstanz, Paris, and Göttingen. I did my PhD at the Max-Planck-Institute and the Ludwig-Maximilians University in Munich on the representation theory of the quantum Poincaré algebra. My advisor was Julius Wess, my coadvisor Hans-Jürgen Schneider. After that, I spent two years as Postdoctoral Fellow and Lecturer at the International University Bremen in the group of Peter Schupp. Since 2005, I am Marie-Curie Fellow at the Math Department of the University of California, Berkeley. My mentor here is Alan Weinstein.

Research Interests

My general interests are in Symplectic Geometry, Noncommutative Geometry, Quantization, Representation Theory, and Mathematical Physics. My work deals with quantization problems, generalized geometrical structures, and noncommutative geometry. I study generalized geometrical structures and the corresponding symmetry structures, such as Lie algebroids, groupoids, 2-groups and 2-groupoids, differentiable stacks, Dirac structures, Hopfish algebras, quantum groups and quantum enveloping algebras. One of my long-term projects is to understand how noncommutative configuration space geometry can arise naturally from quantizing classical mechanical systems with singularities such as magnetic monopoles or spacetime singularities. My currently active projects are:
  • Stacky Lie groups
  • Hopfish algebras (with Xiang Tang and Alan Weinstein)
  • Noncommutative geometry and quantization of Poisson manifolds with singularities
  • Groupoid symmetries of spacetime covariant field theories (with Marco Cezar Fernandez and Alan Weinstein)
Earlier projects dealt with noncommutative differential calculus and wave equations on quantum Minkowski space (with Fabian Bachmaier), the calculation of universal Drinfeld twists, the algebraic structure and representation theory of the quantum Poincare algebra, and the construction of theories of gravity on noncommutative spaces (with Paolo Aschieri, Marija Dimitrijevic, Frank Meyer, Peter Schupp, and Julius Wess).

Publications

Research papers

  1. Stacky Lie groups
    math.SG/0701499
  2. Group-like objects in Poisson geometry and algebra
    (with Alan Weinstein)
    math.SG/0701499, accepted for publication in Contemp. Math.
  3. Hopfish structure and modules over irrational rotation algebras
    (with Xiang Tang and Alan Weinstein)
    math.qa/0604405, accepted for publication in Contemp. Math.
  4. Separation of noncommutative differential calculus on quantum Minkowski space
    (with Fabian Bachmaier)
    J. Math. Phys. 47 (2006), no. 2, 023501, 22 pp., math.qa/0506249
  5. A Gravity theory on noncommutative spaces
    (with P. Aschieri, M. Dimitrijevic, F. Meyer, P. Schupp, and J. Wess)
    Class. Quant. Grav. 22 (2005), 3511-3532, hep-th/0504183
  6. Reconstruction of universal Drinfeld twists from representations
    J. Math. Phys. 46 (2005), no. 5, 053519, 17 pp., math.qa/0410448
  7. Computation of the universal Drinfeld twist for quantum su(2)
    in: Noncommutative geometry and representation theory in mathematical physics,
    Contemp. Math. 391 (2005), 11-19
  8. Perturbative symmetries on noncommutative spaces
    Int. J. Mod. Phys. A19 (2004), no. 32, 5693-5706, math.qa/0402200
  9. Realization of q-deformed spacetime as star product by a Drinfeld twist
    in: GROUP 24: Physical and Mathematical Aspects of Symmetries,
    IoP Conference Series 173, 443-446, math.QA/0402199
  10. Covariant realization of quantum spaces as star products by Drinfeld twists
    J. Math. Phys. 44 (2003), 4736-4755, math.QA/0209180
  11. Free q-deformed relativistic wave equations by representation theory
    Eur. Phys. J. 30 (2003), 435-445, hep-th/0111172
  12. Spin in the q-Poincaré algebra
    Commun. Math. Phys. 243 (2003), 329-342, math.QA/0111008

PhD thesis

Lists of most of my papers can also be found on the arXiv, MathSciNet (access may be restricted), and SPIRES.

Teaching

Spring 2007

Math 290: Symplectic geometry seminar (with Alan Weinstein)
Monday from 2:10 to 3:30, Room 72 Evans Hall.

Past courses

Berkeley:

Fall 2006:
Instructor: Math 242 - Symplectic Geometry, Course Webpage
Math 290: Symplectic geometry seminar (with Alan Weinstein)

Fall 2005:
Math 242 - Symplectic Geometry (teaching assistant, course taught by Alan Weinstein)

International University Bremen:

Fall 2004:
Instructor: Math 431 - Lie Groups and Lie Algebras

Interdisciplinary

  • Der rechnende Dichter (The Calculating Poet)
    invited speech on mathematics in German literature, Studienstiftung des deutschen Volkes, Munich, 16 Feb. 2000,
    math.HO/0308287
  • Dichter, Mathematiker und Sterndeuter. Hermann Brochs ``Unbekannte Größe'' (with A. Albrecht)
    invited talk at the public symposion ``Stars and Literature in the 20th centrury'', Basel University, 15 Jan. 2004
    to be published in: ``Gestirn und Literatur im 20. Jahrhundert'', edited by M. Bergengruen et al., Frankfurt am Main: Fischer Verlag 2005
  • Einsteins neue Geometrien (Einstein's new geometries)
    invited talk, Philologischer Salon, Göttingen, 14 Jan. 2005
Last updated: 4 Nov 2006