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Vorträge

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Vorträge 2017

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13 Einträge gefunden

Seite 1 von 2 12 >>

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

    Julian Külshammer, Stuttgart: Ringel duality as a special case of Koszul duality

    Quasi-hereditary algebras are a class of finite dimensional algebras which occur frequently in representation theory. Prominent examples are blocks of BGG category O as well as Schur algebras of reductive algebraic groups. In 1991, Ringel constructed a duality on the class of quasi-hereditary algebras using a characteristic tilting module. Koszul duality dates back to a 1978 paper by Bernstein, Gelfand, and Gelfand which provides an equivalence between the bounded derived categories of a symmetric and an exterior algebra. In this talk, we show how to interpret Ringel duality as a special case of Koszul duality for differential graded algebras. This is joint work with Agnieszka Bodzenta which is based on ideas of Sergiy Ovsienko.

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

    Baptiste Rognerud, IRMA Strasbourg: A Morita theory for permutation modules

    It is known that the trivial source modules (or p-permutation modules) over a block of group algebra share a lot of similarities with the projective modules. For example, there are only finitely many of them, and working over a p-modular system, any trivial source module over the field of positive characteristic lifts uniquely to a trivial source module over the valuation ring. It has also been shown by Arnold that it is possible to do homological algebra with this family of modules.

    The aim of the talk is to explain what happens when you replace projective modules by trivial source modules in the classical Morita theory between blocks of group algebras. This is a joint work with Markus Linckelmann.

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

    Wolfgang Willems, Magdeburg: On quasi-projective Brauer characters

    We study p-Brauer characters of a finite group G which are restrictions of generalized characters vanishing on p-singular elements for a fixed prime p dividing the order of G. Such Brauer characters are called quasi-projective. We show that for each irreducible Brauer character there exists a minimal p-power, say pa(φ), such that pa(φ) φ is quasi-projective. The exponent a(φ) only depends on the Cartan matrix of the block to which  φ belongs. Moreover pa(φ)   is bounded by the vertex of the module afforded by φ, and equality holds in case that G is p-solvable. We give some evidence for the conjecture that  a(φ) occurs if and only if  φ belongs to a block of defect 0. Finally, we study indecomposable quasi-projective Brauer characters of a block B. This set is finite and corresponds to a minimal Hilbert basis of the rational cone defined by the Cartan matrix of B.

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

    William Wong,TU Kaiserslautern: A phenomenon in the representation of SL(2,q) in defining

    I will talk about my PhD research, which uncovers some properties of modules of SL(2,q) in defining characteristics. It heavily depends on information from representations of its Borel subgroup, which is equivalent to the normaliser of the defect group in this case. In this talk I will present the results using combinatorial properties in the local representation.

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

    Andreas Bächle, University Brussels: Rationality of groups and centers of integral group rings

    A finite group is called rational if all entries of its character table are rational integers. Being rational has significant implications for the structure of the group, e.g. it is a classical result of R. Gow that the only primes dividing the order of such a group are 2, 3 and 5, if the group is solvable. The concept of rationality was generalized in 2010 by D. Chillag and S. Dolfi by introducing the term (inverse) semi-rational group. It turned out that being an inverse semi-rational group has quite some impact in the study of integral group rings. We will discuss this connection and recent results.

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

    Emil Norton, MPI Bonn: The sl_∞-crystal combinatorics of higher level Fock spaces

    A crystal is a type of directed graph encoding representation theoretic information. The crystal I will discuss is called the Heisenberg or <nobr></nobr> crystal, originally defined by Shan and Vasserot. Its vertices are multipartitions, and its arrows arise from a categorical action of a Heisenberg algebra on cyclotomic Cherednik category O. The representation theoretic meaning of this crystal is to keep track of one part of the support of simple modules. There are two crystals needed to determine supports; the other is the <nobr></nobr> crystal. Likewise, Dudas-Varagnolo-Vasserot recently constructed categorical actions of these two crystals on the unipotent category of finite classical groups in order to classify Harish-Chandra series. The problem of computing the arrows in the <nobr></nobr> crystal was reduced to a combinatorial problem by Thomas Gerber. I will explain the solution to this problem: the rule for the arrows, and the rule for determining depth of a multipartition in the crystal. This is joint work with Thomas Gerber.

     

     

     

  • April
  • 27. April
    17:00 - 18:00
    Ort: 48-436
    Algebra, Geometry and Computer Algebra

    Kivanv Ersoy, TU Kaiserslautern: Locally finite groups with small centralizers

    In this talk we will present recent results about fixed points of automorphisms in locally finite groups. Let pbe a prime and  G a locally fi nite group containing an elementary abelian p-subgroup A of rank at least 3 such that CG (A) is Chernikov and CG (a) involves no infi nite simple groups for any a ∈ A#. We show that G is almost locally soluble. To prove this result, we first give a characterization of PSLp (k). Theorem. [1] An infi nite simple locally fi nite group G admits an elementary abelian p-group of automorphisms A such that CG (A) is Chernikov and CG (a) involves no in finite simple groups for any a ∈ A# if and only if G is isomorphic to PSLp (k) for some locally finite field k of characteristic diff erent from p and A  has order <nobr> p2. This is a joint work with Mahmut Kuzucuoglu and Pavel Shumyatsky.
    [1] Ersoy, K., Kuzucuoglu, M., Shumyatsky, P., Locally finite groups and their subgroups with small centralizers, J. Algebra, Vol. 481, 1 July 2017, p.1-11. ρ

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

    Michael Geline, Northern Illinois University: Some quantitative and qualitative aspects of Knörr lattices

    These lattices are the <nobr></nobr> p-adic representations of finite groups whose invertible endomorphisms can be distinguished by the trace function. They include the absolutely irreducible lattices as well as the indecomposable lattices of rank not divisible by p. Knörr introduced them in a 1988 paper in connection with Brauer's height zero conjecture. They are now known also to be connected with Alperin's weight conjecture. I will explain this in the talk, and, time permitting, also give a quantitative result: Knörr lattices for the elementary abelian group of order 8, over an dvr unramified over the 2-adics, do not exist.

  • Februar
  • 23. Februar
    16:00 - 17:00
    Ort: 48-436
    AG Algebra, Geometrie und Computer Algebra

    Prof. Dr. Eugenii Shustin, Tel Aviv University; Real morsifications of plane curve singularities.

    A real morsification of a real plane curve singularity is a real deformation with the maximal possible number of hyperbolic nodes (i.e., equivalent to x2-y2=0 over R). We prove that any real plane curve singularity admits a real morsification. This was known before only in the case of all local branches being real (A'Campo, Gussein-Zade). We also discuss a relation between real morsifications and the topology of singularities and extend to arbitrary real morsifications the Balke-Kaenders theorem stating that the A'Campo--Gussein-Zade diagram associated to the morsification uniquely determines the real topological type of the initial curve singularity. Joint work with Piter Leviant.

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

    Charles Eaton, University of Manchester: Loewy length of blocks

    I will give a brief survey on results and conjectures about the Loewy length of a block of a finite group. This includes work with Michael Livesey giving precise upper and lower bounds for 2-blocks with abelian defect groups.

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