2 entries found

• January
• 25. January

  17:00 - 18:00
  

  Location: 48-436
  AG Algebra, Geometrie und Computer Algebra

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

  Category: AG Algebra, Geometrie und Computeralgebra

  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. January

  17:00 - 18:00
  

  Location: 48-436
  AG Algebra, Geometrie und Computer Algebra

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

  Category: AG Algebra, Geometrie und Computeralgebra

  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.