Talks in 2003

  • 18.12.2003, Jan Schröer (Leeds)
    (Dual)(semi)canonical bases and preprojective varieties
    Abstract: The main topic of the talk will be the geometric construction of bases of simple representations over finite-dimensional simple complex Lie algebras. One of these bases, namely Lusztig's semicanonical basis, is closely related to the representation theory of preprojective algebras. This will be discussed in detail.
  • 27.11.2003 (16.15 Uhr), Øyvind Solberg (Trondheim)
    The chromatic tower of D(R), IV
    Abstract: This is a continuation of the series of lectures on Neeman's paper.
  • 20.11.2003 (16:45), Hagen Meltzer (Stettin)
    Indecomposable modules for domestic canonical algebras
    Abstract (in PDF-format)
  • 20.11.2003 (15:15 Uhr), Miles Holloway (Oxford)
    Broue's conjecture through computer calculations
    Abstract: I will talk about my thesis and verifying Broue's conjecture for the Hall-Janko group.
  • 13.11.2003 (16.15 Uhr), Miles Holloway (Oxford)
    The chromatic tower of D(R), III
    Abstract: This is a continuation of the series of lectures on Neeman's paper.
  • 13.11.2003 (15:15 Uhr), Dirk Kussin (Paderborn)
    The chromatic tower of D(R), II
    Abstract: We present §1 of Neeman's paper which contains the proof of the Nilpotence Theorem.
  • 06.11.2003, Henning Krause (Paderborn)
    The chromatic tower of D(R), I
    Abstract: This is the first in a series of talks on work of Hopkins and Neeman, following the paper "The chromatic tower of D(R)" by Amnon Neeman [Topology 31 (1992) , 519-532]. In the first part, I will describe an explicit construction of the unbounded derived category D(R) of a ring R, using K-projective and K-injective resolutions (in the terminology of Spaltenstein) for unbounded complexes. There are also some notes available (in PS Format).
  • 30.10.2003, Andrew Hubery (Paderborn)
    The composition monoid of the Kronecker algebra
    Abstract: Reineke first introduced the composition monoid as a tool for understanding extensions between representations of the Dynkin quivers. He later extended the definition to include all quivers by considering extensions between families of representations. Here we consider the special case of the Kronecker quiver and determine defining relations for the composition monoid. We also obtain a normal form for the varities occurring in the composition monoid in terms of Schur roots.
  • 16.10.2003, Christof Geiss (UNAM, Mexico)
    Die universelle Übererlagerung einer präprojektiven Algebra
    Abstract: Wir berichten über die Ergebnisse einer Diskussion mit Henning Krause. Sei A eine endlichdimensionale zusammenhängende darstellungsendliche hereditäre Algebra, und P die zugehörige präprojektive Algebra. Wir betrachten die übliche Galoisüberlagerung G von P. Die Identifikation von Add(G) mit der derivierten Kategorie von A-mod, einer triangulierten Kategorie, führt zu interessanten Formeln für die Auslander-Reiten Verschiebung in G-mod. Andererseits beobachten wir, dass G auch die repetitive Algebra der stabilen Auslanderalgebra T von A ist. T ist genau dann quasigekippt, wenn die Coxeterzahl von A höchstens 6 ist. Zusammen mit den oben erwähnten Formeln erklärt dies das gute Verständnis von P in diesen Fällen.
  • Dienstag, 14.10.2003 im Rahmen des Mathematischen Kolloquiums: 17.45 Uhr, Hörsaal D 2
    Jon F. Carlson (Univ. of Georgia, MPI Bonn)
    The coclass classification of p-groups
    Abstract: The classificiation of finite simple groups is one of the most celebrated accomplishments of mathematics of the last century. Less well known is a recent classification of finite p-groups, groups whose elements all have order a power of a prime p. This was accomplished by Leedham-Green and several others. In this classification the p-groups are sorted into families associated to objects called uniserial p-adic space groups. The space groups and the families can be reasonably described in terms of matrix groups. A large part of the lecture will be devoted to explaining the classification. Then the question is how do we use it?

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