dbar complex analysis univie_logo_schwarz_web

People Projects Teaching Diploma PhD Activities Location

Contact Information

Phone 0043-(0)1-4277-50749
Fax 0043-(0)1-4277-50750
Office AN 110
Postal address Department of Mathematics
University of Vienna
Nordbergstrasse 15
1090 Vienna

Research Interests

My research is concerned with the commutative and non-commutative geometry of symplectic quotients. I am focusing on the cases of taking the quotient at singular levels of the moment map. A prototypical example is reduction at zero of a moment map of a unitary representation of a compact Lie group. I am working on the isomorphism problem for such symplectic quotients and try to understand when such spaces are symplectomorphic to a finite unitary quotient. Moreover, I am concerned with the problem of quantization of symplectic quotients and the study of commutative algebraic properties of quadratic moment maps.


Selected Publications

[8] The Hilbert series of a linear symplectic circle quotient (H.-C. Herbig, C. Seaton), In ArXiv e-prints, 2013. [bib]
[7] The Koszul complex of a moment map (H.-C. Herbig, G. W. Schwarz), In Journal of Symplectic Geometry (accepted for publication), 2012. [bib]
[6] On orbifold criteria for symplectic toric quotients (C. Farsi, H.-C. Herbig, C. Seaton), In Symmetry, Integrability and Geometry: Methods and Applications (accepted for publication), 2012. [bib]
[5] On the existence of star products on quotient spaces of linear Hamiltonian torus actions (H.-C. Herbig, Srikanth B. Iyengar, Markus J. Pflaum), In Lett. Math. Phys., volume 89, 2009. [bib] [pdf] [doi]
[4] A homological approach to singular reduction in deformation quantization (Martin Bordemann, H.-C. Herbig, Markus J. Pflaum), Chapter in Singularity theory, World Sci. Publ., Hackensack, NJ, 2007. [bib] [pdf] [doi]
[3] Variations on Homological Reduction (H.-C. Herbig), PhD thesis, , 2007. [bib]
[2] Formalite $G^infty$ adaptee et star-representations sur des sous-varietes coisotropes (M. Bordemann, G. Ginot, G. Halbout, H.-C. Herbig, S. Waldmann), In ArXiv Mathematics e-prints, 2005. [bib]
[1] BRST cohomology and phase space reduction in deformation quantization (Martin Bordemann, H.-C. Herbig, Stefan Waldmann), In Comm. Math. Phys., volume 210, 2000. [bib] [pdf] [doi]
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Offenlegung nach Par. 25 Mediengesetz: Für den Inhalt verantwortlich: Fakultät für Mathematik, Universität Wien