Prof. Dr. Gerhard Röhrle

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Arbeitsgebiete

  • 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").
     
  • Publications on MathSciNet.

  • Recent preprints on the ArXiv.
     
  • Latest preprints:

    Inductive and Recursive Freeness of Localizations of Multiarrangements

    with T. Hoge and A. Schauenburg
    Abstract:
    The class of free multiarrangements is known to be closed under taking localizations. We extend this result to the stronger notions of inductive and recursive freeness. As an application, we prove that recursively free multiarrangements are compatible with the product construction for multiarrangements. In addition, we show how our results can be used to derive that some canonical classes of free multiarrangements are not inductively free.
    math.CO/1501.06312

    Inductively free Multiderivations of Braid arrangements

    with H. Conrad
    Abstract:
    The reflection arrangement of a Coxeter group is a well known instance of a free hyperplane arrangement. In 2002, Terao showed that equipped with a constant multiplicity each such reflection arrangement gives rise to a free multiarrangement. In this note we show that this multiarrangment satisfies the stronger property of inductive freeness in case the Coxeter group is of type A.
    math.CO/1502.02393

    Cocharacter-closure and the rational Hilbert-Mumford Theorem

    with M. Bate, S. Herpel, and B. Martin
    Abstract:
    For a field k, let G be a reductive k-group and V an affine k-variety on which G acts. Using the notion of cocharacter-closed G(k)-orbits in V, we prove a rational version of the celebrated Hilbert-Mumford Theorem from geometric invariant theory. We initiate a study of applications stemming from this rationality tool. A number of examples are discussed to illustrate the concept of cocharacter-closure and to highlight how it differs from the usual Zariski-closure.
    math.GR/1411.7849

    Addition-Deletion Theorems for Factorizations of Orlik-Solomon Algebras and nice Arrangements

    with T. Hoge
    Abstract:
    We study the notion of a nice partition or factorization of a hyperplane arrangement due to Terao from the early 1990s. The principal aim of this note is an analogue of Terao's celebrated addition-deletion theorem for free arrangements for the class of nice arrangements. This is a natural setting for the stronger property of an inductive factorization of a hyperplane arrangement by Jambu and Paris. In addition, we show that supersolvable arrangements are inductively factored and that inductively factored arrangements are inductively free. Combined with our addition-deletion theorem this leads to the concept of an induction table for inductive factorizations. Finally, we prove that the notions of factored and inductively factored arrangements are compatible with the product construction for arrangements.
    math.CO/1402.3227


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    Former and current PhD students:
    Simon Goodwin (University of Birmingham)
    Michael Bate (University of York)
    Russell Fowler (Npower)
    Glenn Ubly (NHS)
    Sebastian Herpel
    Peter Mosch (Gothaer Lebensversicherung AG)
    Nils Amend
    Anne Schauenburg


    Editorial Activity:

    Tbilisi Mathematical Journal .

    Computer Programs