Bildarchiv des Mathematischen Forschungsinstituts Oberwolfach


  • Algebraische Lie Theorie
  • Algebraische Gruppen
  • Darstellungstheorie
  • Endliche Gruppen vom Lie-Typ
  • Hyperebenenarrangements
  • Spiegelungsarrangements

  • DFG project: Serre's notion of Complete Reducibility and Geometric Invariant Theory (within the DFG Priority Programme in Representation Theory).
  • DFG project: Computational aspects of the Cohomology of Coxeter arrangements: On Conjectures of Lehrer-Solomon and Felder-Veselov (within the DFG Priority Programme "Algorithmic and experimental methods in Algebra, Geometry and Number Theory").
  • DFG project: Arrangements of complex reflection groups: Geometry and combinatorics (joint with M. Cuntz (Kaiserslautern) within the DFG Priority Programme "Algorithmic and experimental methods in Algebra, Geometry and Number Theory").
  • DFG project: Inductive freeness and rank-generating functions for arrangements of ideal type: Two conjectures of Sommers and Tymoczko revisited (within the DFG GEPRIS).
  • Publications on MathSciNet.

  • Recent preprints on the ArXiv.
  • Latest preprints:

    Some remarks on free arrangements

    with T. Hoge
    We exhibit a particular free subarrangement of a certain restriction of the Weyl arrangement of type E7 and use it to give an affirmative answer to a recent conjecture by T. Abe on the nature of additionally free and stair-free arrangements.

    Relative complete reducibility and normalised subgroups

    with M. Gruchot and A. Litterick
    We study a relative variant of Serre's notion of G-complete reducibility for a reductive algebraic group G. We let K be a reductive subgroup of G, and consider subgroups of G which normalise the identity component K^o. We show that such a subgroup is relatively G-completely reducible with respect to K if and only if its image in the automorphism group of K^o is completely reducible. This allows us to generalise a number of fundamental results from the absolute to the relative setting. We also derive analogous results for Lie subalgebras of the Lie algebra of G, as well as `rational' versions over non-algebraically closed fields.

    A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups

    with T. Abe, C. Stump and M. Yoshinaga
    Given an irreducible well-generated complex reflection group, we construct an explicit basis for the module of vector fields with logarithmic poles along its reflection arrangement. This construction yields in particular a Hodge filtration of that module. Our approach is based on a detailed analysis of a flat connection applied to the primitive vector field. This generalizes and unifies analogous results for real reflection groups.

    The K(pi,1)-problem for restrictions of complex reflection arrangements

    with Nils Amend and Pierre Deligne
    Let W in GL(V) be a complex reflection group, and A(W) the set of the mirrors of the complex reflections in W. It is known that the complement X(A(W)) of the reflection arrangement A(W) is a K(pi,1) space. For Y an intersection of hyperplanes in A(W), let X(A(W)^Y) be the complement in Y of the hyperplanes in A(W) not containing Y. We hope that X(A(W)^Y) is always a K(pi,1). We prove it in case of the monomial groups W=G(r,p,l). Using known results, we then show that there remain only three irreducible complex reflection groups, leading to just eight such induced arrangements for which this K(pi,1) property remains to be proved.


    Former and current PhD students:
    Simon Goodwin (University of Birmingham)
    Michael Bate (University of York)
    Russell Fowler (Npower)
    Glenn Ubly (NHS)
    Sebastian Herpel (Barmenia Allgemeine Versicherungs-AG)
    Peter Mosch (Gothaer Lebensversicherung AG)
    Nils Amend (INTER Krankenversicherung AG)
    Anne Schauenburg
    Maike Gruchot
    Tilman Möller
    Falk Bannuscher

    Editorial Activity:

    Tbilisi Mathematical Journal .

    Computer Programs