Universität Jena, Fakultät für Mathematik & Informatik, Lehrstuhl Algebra

Oberseminar Algebra/Zahlentheorie - Vorträge 2013


WS 2013/2014

Dienstag, den 17. Dezember 2013, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2
PD Dr. Jürgen Müller,   (Universität Jena)
"Vertices of Lie modules"
Abstract:The Lie module LieF(n) of the symmetric group Sn over a field F of characteristic p>0 is the left ideal of FSn generated by the so-called Dynkin-Specht-Wever element ωn. We study the problem of describing the non-projective indecomposable summands of LieF(n), in particular their vertices and sources. Our main result shows that this can be reduced to the case when n is a power of p. When n=9 and p=3, and when n=8 and p=2, we present a precise answer, suggesting a description for arbitrary prime powers. This is joint work with Roger Bryant, Susanne Danz and Karin Erdmann.
Dienstag, den 10. Dezember 2013, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2
Prof. David Green,   (Universität Jena)
"Koprime Operationen auf der Sylow p-Untergruppe der symmetrischen Gruppe S_{p^n}"
Dienstag, den 03. Dezember 2013, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2
Dr. Guido Pezzini,   (Universität Erlangen)
"On the B-orbits of some spherical homogeneous spaces"
Abstract:: Schubert cells and Schubert varieties play a central role in the study of the geometry of flag varieties and in the theory of reductive algebraic groups. In the talk, reporting on a joint work with Jacopo Gandini, we will discuss such objects in the setting of spherical varieties, which generalize flag varieties as well as toric and symmetric ones.
We will focus in particular on the case of a homogeneous space G/H, where G is a complex reductive group and H is a solvable subgroup. The set B(G/H) of its Schubert cells, i.e. its B-orbits where B is a Borel subgroup of G, can be combinatorially described in terms of the so-called Luna invariants of G/H. We will explain this description, together with its interplay with other relevant structures on B(G/H), such as the action of the Weyl group of G on B(G/H) defined by F. Knop.
Dienstag, den 19. November 2013, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2
Dr. Attila Maróti ,   (University of Budapest; z.Zt. Uni. Kaiserslautern)
"On finite linear group actions"
Abstract: : Let V be a finite faithful irreducible G-module for some finite group G. A base B is a subset of V with the poperty that the joint stabilizer in G of all vectors in B is the identity. The minimal size of a base is denoted by b(G).
There are many results on b(G) and such theorems, in case G is solvable, have applications to Gluck's conjecture, say. This is the following. Let H be a finite solvable group and let F(H) be its Fitting subgroup (the largest nilpotent normal subgroup of H). Then |H:F(H)| is at most the square of the largest complex irreducible character degree of H.
In the first part of my talk I will briefly mention what the non-coprime k(GV) problem is. The second part of my talk (minimal base sizes) will be on a recent work of mine with Zoltan Halasi. In the third part (on Gluck's conjecture) I will report on a joint work with James P. Cossey, Zoltan Halasi and Hung Ngoc Nguyen.
Dienstag, den 05. November 2013, in JENA, SR 3517, Ernst-Abbe-Platz 2
Gemeinsames Oberseminar mit dem Mathematischen Institut der Universität Halle-Wittenberg
14:15-15:15 Uhr Dipl.-Math. Johannes Hahn   (Universität Jena)
"Struktureigenschaften von W-Graphen"
15:15-15:45 Uhr Kaffeepause
15:45-16:45 Uhr Dipl.-Math. Christian Pröseler   (Universität Halle-Wittenberg)
"Gruppen von parabolischer Charakteristik 2
17:00-18:00 Uhr Prof. Yuanyang Zhou   (Central China Normal University, Wuhan, z. Zt. Universität Jena)
"Glauberman correspondents and blocks with Klein four defect groups"
Dienstag, den 29. Oktober 2013, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2
Prof. Oksana Yakimova,   (Universität Jena)
"On commutative subalgebras of the universal enveloping algebra"
Dienstag, den 22. Oktober 2013, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2
Prof. Alexandre Zalesski,   (Minsk (Weißrussland); z.Zt. Hausdorff Institut Bonn)
"The restriction of the Steinberg representation of an orthogonal group to orthogonal subgroups of one less dimension"
Abstract: Let V be a vector space of dimension n over a finite field F, and let H=SO(V) be the special orthogonal group. Let V' be a non-degenerate subspace of V of dimension n-1 and G=SO(V'). Let St_H be the Steinberg representation of H (over the complex numbers).
We will discuss the following theorem: every irreducible constituent of the restriction St_H to G occurs with multiplicity at most 2, and if n is even then all multiplicities are equal to 1. It is also planned to comment on a relation of this result with projective modules for G (over F).
Dienstag, den 15. Oktober 2013, 14:15 Uhr, SR 3517, Ernst-Abbe-Platz 2
Prof. Alfons Ooms,   (Hasselt University, Belgien)
"The Poisson center and maximal commutative subalgebras for a Lie algebra"
Abstract: Let L be a finite dimensional Lie algebra over a field k of characteristic zero and let S(L) be its symmetric algebra, equipped with its natural Poisson structure. First we recall some basic notions about Lie algebras and then we collect some general facts on the Poisson center of S(L), including some simple criteria regarding its polynomiality, and also on certain Poisson commutative subalgebras of S(L). These facts allow us to give an explicit description for the Poisson center for all complex, nilpotent Lie algebras of dimension at most seven. Among other things, we also provide in each case a polynomial, maximal Poisson commutative subalgebra of S(L), enjoying additional properties. As a by-product we show that a conjecture by Milovanov is valid in this situation.

SS 2013

Dienstag, den 09. Juli 2013, 14:15 Uhr,
"Mathematik in der Natur"
Dienstag, den 02. Juli 2013, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2
Prof. Hideto Asashiba,   (Shizuoka University, Japan; z.Zt. MPI für Mathematik Bonn)
"Colax actions of a category and gluing of derived equivalences"
Dienstag, den 25. Juni 2013, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2
Dr. Willem de Graaf,   (Dipartimento di Matematica, University of Trento, Italy)
"Listing nilpotent orbits of real simple Lie algebras"
Abstract:The nilpotent orbits of a real simple Lie algebra are in bijection with the nilpotent orbits related to a certain symmetric pair; this is known as the Kostant-Sekiguchi correspondence. In this talk I will describe algorithms for carrying out one direction of this correspondence. Together with algorithms for obtaining the nilpotent orbits in the isotropy representation of a symmetric space (which is a special case of a theta-group), this yields a method to list the nilpotent orbits of a real simple Lie algebra.
Donnerstag, den 20. Juni 2013, 16:15 Uhr, SR 121 Carl-Zeiss-Str. 3
Prof. Andrew Chermak,   (Kansas State University)
"The structure of p-local finite groups"
Dienstag, den 18. Juni 2013, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2
Prof. Dr. Ivan Penkov,   (Jacobs University Bremen)
"Lie algebras of infinite matrices and their representations"
Abstract: pdf-Datei
Dienstag, den 04. Juni 2013,
Gemeinsames Oberseminar mit dem Mathematischen Institut der Universität Halle-Wittenberg
Einladung
Dienstag, den 21. Mai 2013, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2
Dr. Caroline Lassueur   (TU Kaiserslautern)
"Reading endotrivial modules in the Brauer tree"
Abstrakt: If G is a finite group and k a field of prime characteristic p, a kG-module is termed "endo-trivial" if its k-endomorphism ring decomposes as a direct sum of a copy of the trivial module and projective summands. In this talk we explain how to determine whether or not a simple kG-module is endo-trivial by looking at its position in the Brauer tree. We will explain why this an important special case of the classification of simple endo-trivial modules (for quasi-simple groups).
Dienstag, den 14. Mai 2013, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2
Prof. Klaus Altmann   (FU Berlin)
"Toric varieties - deformations, resolutions, and quotients"
Dienstag, den 07. Mai 2013,
Gemeinsames Oberseminar mit dem Mathematischen Institut der Universität Halle-Wittenberg
14:15-15:15 Uhr Prof. Dmitri Panyushev   (Moskau, z. Zt. Universität Jena)
"Abelian ideals of a Borel subalgebra: combinatorics and geometry"
Kaffeepause
15:45-16:45 Uhr Frau Dipl.-Math. Imke Toborg   (Universität Halle-Wittenberg)
"3'-Groups from a local point of view"
17:00-18:00 Uhr Prof. Burkhard Külshammer   (Universität Jena)
"Blocks of finite groups: structure and local properties"
Dienstag, den 30. April 2013, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2
Prof. Yuanyang Zhou   (Central China Normal University, Wuhan, China; z. Zt. FSU Jena)
"Extensions of trivial inertial blocks"
Dienstag, den 23. April 2013, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2
Prof. Dr. Wolfgang Willems   (Otto-von-Guericke-Universität Magdeburg)
"Characterization of groups via dimensions of PIM's"
Dienstag, den 16. April 2013, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2
Prof. O. Yakimova   (Universität Jena)
"Orbit closures in θ-representations "
Dienstag, den 09. April 2013, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2
Prof. O. Yakimova   (Universität Jena)
"Orbit closures and θ-representations "

WS 2012/13

Dienstag, den 15. Januar 2013, in HALLE/Saale, SR 3, Georg-Cantor-Haus, Theodor-Lieser-Str. 5
Gemeinsames Oberseminar mit dem Mathematischen Institut der Universität Halle-Wittenberg
Dienstag, den 08. Januar 2013, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2
Tim Fritzsche   (Universität Jena)
"Der Darstellungstyp des Charakterrings einer endlichen Gruppe"


Autor: <Ines.Spilling (at) uni-jena.de>.
Zuletzt geändert am 24.03.2014