### Contact Information

herbig(at)qgm.au.dk | |

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 Austria |

### 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.

**CV**

### Selected Publications

2013 | |

[8] | The Hilbert series of a linear symplectic circle quotient , In ArXiv e-prints, 2013. [bib] |

2012 | |

[7] | The Koszul complex of a moment map , In Journal of Symplectic Geometry (accepted for publication), 2012. [bib] |

[6] | On orbifold criteria for symplectic toric quotients , In Symmetry, Integrability and Geometry: Methods and Applications (accepted for publication), 2012. [bib] |

2009 | |

[5] | On the existence of star products on quotient spaces of linear Hamiltonian torus actions , In Lett. Math. Phys., volume 89, 2009. [bib] [pdf] [doi] |

2007 | |

[4] | A homological approach to singular reduction in deformation quantization , Chapter in Singularity theory, World Sci. Publ., Hackensack, NJ, 2007. [bib] [pdf] [doi] |

[3] | Variations on Homological Reduction , PhD thesis, , 2007. [bib] |

2005 | |

[2] | Formalite $G^infty$ adaptee et star-representations sur des sous-varietes coisotropes , In ArXiv Mathematics e-prints, 2005. [bib] |

2000 | |

[1] | BRST cohomology and phase space reduction in deformation quantization , In Comm. Math. Phys., volume 210, 2000. [bib] [pdf] [doi] |

Offenlegung nach Par. 25 Mediengesetz: Für den Inhalt verantwortlich: Fakultät für Mathematik, Universität Wien