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<< April 2015

Veranstaltungskalender Mai 2015

Juni 2015 >>

3 Einträge gefunden

  • 12. Mai
    15:30 - 16:30
    Ort: 48-436
    AG Algebra, Geometrie und Computeralgebra

    Danny Neftin (University of Michigan, Ann Arbor): Monodromy groups of rational functions

    A fundamental invariant associated to every rational function is its monodromy group. We shall discuss the accumulating group theoretic work towards determining the complex rational functions with a specified monodromy group, and its applications to problems concerning values of rational functions over finite fields, Hilbert irreducibility, Nevanlinna theory, and Mazur's torsion theorem.

  • 21. Mai
    15:30 - 16:30
    Ort: 48-438
    AG Algebra, Geometrie und Computeralgebra

    Andreas Steepaß (TU Kaiserslautern): Semaphores

    Semaphores are data structures which can be used to manage restricted
    resources in concurrent programming. For example, Singular's parallel
    framework uses a semaphore to ensure that the number processes running
    in parallel is bounded by some user-definable integer. In this talk, we
    will first show how basic synchronisation patterns such as mutexes,
    rendezvous, and barriers can be implemented by means of semaphores.
    Based on these ingredients, we will then focus on more complicated
    situations such as the readers-writers problem or the dining
    philosophers problem. The challenge is to find elegant solutions which
    do not cause deadlocks or starvation.

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

    Vivien Ripoli (Universität Wien): Coxeter elements in well-generated complex reflection groups

    Coxeter elements are specific elements in a reflection group W, that play a key role in Coxeter-Catalan combinatorics, in particular in the construction of the W-noncrossing partition lattice. Several non-equivalent definitions coexist in the literature. I will explain and motivate the following: for W an irreducible real reflection group, or a well-generated complex reflection group, a Coxeter element in $W$ is an element having an eigenvalue of order h (where $h$ is the highest invariant degree of $W$, also known as Coxeter number). The set of these elements does not always form a unique conjugacy class, but it forms a unique orbit under the action of reflection automorphisms of W. Using a Galois action on these elements, we obtain that the number of conjugacy classes is equal to the degree of the field of definition of $W$. When $W$ is real, $c$ is a Coxeter element if and only if there exists a simple system $S$ constituted of reflections and such that $c$ is the product of the elements in $S$. Finally I will explain how some of the properties of these Coxeter elements can be extended to Springer-regular elements. (Joint work with Vic Reiner and Christian Stump)