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Vorträge

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Vorträge 2018

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5 Einträge gefunden

  • Mai
  • 17. Mai
    17:00 - 18:00
    Ort: 48-436
    AG Algebra, Geometrie und Computer Algebra

    Zhicheng Feng, TU Kaiserslautern: On the inductive blockwise Alperin weight condition for special linear and unitary groups

    The inductive blockwise Alperin weight condition is a system of conditions whose verification for all non-abelian finite simple groups would imply the blockwise Alperin weight conjecture. This talk will explain how one can obtain the weights of a special linear or unitary group X from the general linear or unitary group and verify the inductive blockwise Alperin weight condition for any unipotent block of X when the prime does not divide the order of Z(X).

  • 07. Mai
    17:00 - 18:00
    Ort: 48-519
    AG Algebra, Geometrie und Computer Algebra

    Thomas Gobet, University of Sydney: Dual and classical generators of Artin groups of spherical type

    The n-strand braid group has two Garside structures, a classical and a dual one, leading to different solutions to the word problem in the group. The corresponding Garside monoids are the classical braid monoid and the Birman-Ko-Lee braid monoid. These monoids exist for any Artin group of spherical type (i.e., attached to a finite Coxeter group).

    The aim of the talk is to explain how to express the generators of an Artin group of spherical type coming from the dual braid monoid (and more generally the simples, that is, the divisors of the Garside element of the dual monoid) in terms of the classical generators: we give a closed formula to express a simple of the dual braid monoid, using combinatorial objects called c-sortable elements (introduced by Reading). It gives a word of shortest possible length in the classical generators representing a simple element of the dual braid monoid. It has as an immediate consequence that the simples of the dual braid monoids are Mikado braids.

  • 03. Mai
    17:00 - 18:00
    Ort: 48-436
    AG Algebra, Geometrie und Computer Algebra

    Keivan Mallahi-Karai, Jacobs University, Bremen: Kirillov's orbit method and the polynomiality of the essential dimension of p-g

    The faithful dimension of a finite group G is defined to be the smallest dimension of a faithful complex representation of G. Aside from its intrinsic interest, the problem of determining the faithful dimension of finite groups is intimately related to the notion of essential dimension, introduced by Buhler and Reichstein.

    The problem of determining the faithful dimension of families of p-groups arising from F_p-points of a nilpotent algebraic group defined over the field of rational numbers has been studied in some special cases, e.g. the Heisenberg and the full upper-triangular unipotent group.

    In this paper, we will use Kirillov’s orbit method to address this problem for a large family of groups. It will be shown that this function is always a piecewise polynomial function along certain “number-theoretically defined” sets, while, in some specific cases, it is given by a uniform polynomial in p.

    This talk is based on a joint work with Mohammad Bardestani and Hadi Salmasian.

  • Januar
  • 25. Januar
    17:00 - 18:00
    Ort: 48-436
    AG Algebra, Geometrie und Computer Algebra

    Petra Schwer, KIT Karlsruhe: Reflection length in affine Coxeter groups

    Affine Coxeter groups have a natural presentation as reflection groups on some affine space. Hence the set R of all its reflections, that is all conjugates of its standard generators, is a natural (infinite) set of generators. Computing the reflection length of an element in an affine Coxeter group means that one wants to determine the length of a minimal presentation of this element with respect to R. In joint work with Joel Brewster Lewis, Jon McCammond and T. Kyle Petersen we were able to provide a simple formula that computes the reflection length of any element in any affine Coxeter group. In this talk I would like to explain this formula, give its simple uniform proof and allude to the geometric intuition behind it.

  • 18. Januar
    17:00 - 18:00
    Ort: 48-436
    AG Algebra, Geometrie und Computer Algebra

    Florian Eisele, University of London: A counterexample to the first Zassenhaus conjecture

    There are many interesting problems surrounding the unit group U(RG) of the ring RG, where R is a commutative ring and G is a finite group. Of particular interest are the finite subgroups of U(RG). In the seventies, Zassenhaus conjectured that any u in U(ZG) is conjugate, in the group U(QG), to an element of the form +/-g, where g is an element of the group G. This came to be known as the "Zassenhaus conjecture". In recent joint work with L. Margolis, we were able to construct a counterexample to this conjecture. In this talk I will give an introduction to the various conjectures surrounding finite subgroups of U(RG), and how they can be reinterpreted as questions on the (non-)existence of certain R(GxH)-modules, where H is another finite group. This establishes a link with the representation theory of finite groups, and I will explain how, p-locally, our example is made up of certain p-permutation modules.