Oberseminar Algebra/Zahlentheorie

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Vortragsankündigungen

SS 2012

Dienstag, den 22. Mai 2012, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Prof. Radha Kessar   (University of Aberdeen)
"Quasi-isolated blocks and Brauer's height zero conjecture"

Dienstag, den 15. Mai 2012, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Carolin Reiche   (Universität Jena)
"Die Tiefe von Young-Untergruppen symmetrischer Gruppen"

Dienstag, den 8. Mai 2012, SR 3517 Ernst-Abbe-Platz 2

Gemeinsames Oberseminar mit dem Mathematischen Institut der Universität Halle-Wittenberg

14:15-15:15 Uhr Prof. Dr. G. Stroth   (Universität Halle-Wittenberg)
"Small modules"
15:45-16:45 Uhr Prof. Dr. K. Magaard   (University Birmingham)
"Representations of finite unipotent groups"
17:00-18:00 Uhr Prof. D. Green   (Universität Jena)
"On Oliver's p-group conjecture"

Dienstag, den 24. April 2012, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Dozent Dmitry Timashev   (Moscow State University)
"Hamiltonian symplectic varieties with invariant Lagrangian subvarieties (joint work with V.S.Zhgoon)"
Abstract: Recall that a smooth manifold (or algebraic variety) M is symplectic, if there is a closed differential 2-form on M, which induces a symplectic form on each tangent space T_pM, where p is a point of M. A submanifold (subvariety) S is Lagrangian, if dim S = (dim M)/2 and for each p in S the symplectic form on T_pM vanishes on T_pS. Similar to the Riemannian situation, one can speak about the group of symplectic automorphisms of M. An action of a Lie (or an algebraic) group G on M is Hamiltonian, if the elements of G act by symplectic automorphisms and some other natural condition (the existence of a moment map), which will be explained in the talk, is satisfied. We are interested in G-invariant Lagrangian subvarieties of M. A typical example is provided by the cotangent bundle M=T^*X of a G-variety X, where X itself, identified with the zero section of T^*X, is an invariant Lagrangian subvariety.
It is well known in symplectic geometry that a symplectic manifold in a neighbourhood of a Lagrangian submanifold is locally isomorphic to the cotangent bundle of this submanifold. This result holds even in the equivariant setting for Hamiltonian actions of compact Lie groups. If we pass from differential geometry to algebraic (or complex-analytic) geometry and replace compact Lie groups with reductive algebraic groups, as a natural counterpart, then the situation becomes more delicate. However, we prove that several important invariants of a Hamiltonian action, such as corank, defect, and the image of the moment map, coincide for a given Hamiltonian variety M and for the cotangent bundle of any invariant Lagrangian subvariety S. The proof is based on deformation of M to the normal bundle of S and on the so-called "local structure theorem", which describes the action of a certain parabolic subgroup on an open subset of the given variety. Some of our results extend to invariant coisotropic subvarieties. There is some hope to obtain important applications in representation theory.

Dienstag, den 17. April 2012, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Dr. Qiong Guo   (Universität Stuttgart)
"On the U−module Structure of Unipotent Specht Modules of Finite General Linear Groups"

WS 2011/12

Donnerstag, den 2.Februar 2012, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Prof. Gerald Schwarz   (University Brandeis)
"Quotients of finite and compact groups acting on Euclidean space"
Abstract: pdf-Datei

Dienstag, den 31. Januar 2012, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Prof. Gregor Kemper   (TU München)
"Invariantentheorie und die Cohen-Macaulay-Eigenschaft"

Mittwoch, den 7. Dezember 2011, 16:15 Uhr, Konferenzraum 3319

Prof. Shigeo Koshitani   (Chiba, Japan)
"Lifting of perfect isometries in block theory of finite groups"

Dienstag, den 4. Oktober 2011, 14:15 Uhr, SR 121 CZ3

Dr. Britta Späth   (Lehrstuhl D für Mathematik, RWTH Aachen)
"Ein Reduktionstheorem für Alperin's Gewichtsvermutung"

Donnerstag, den 22. September 2011, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Prof. Tomoyuki Wada   (Tokyo University of Agriculture and Technology, Japan)
"The heights of irreducible Brauer characters in 2-blocks of the symmetric groups"

Donnerstag, den 8. September 2011, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Prof. Karin Erdmann   (Mathematical Institute at the University of Oxford, UK)
"Komplexität und Varietäten für Moduln einiger endlich-dimensionaler Algebren"

PD Dr. Jürgen Müller   (Universität Duisburg-Essen)
"On the structure of the tensor square of the natural module of the symmetric group"
Abstract:We determine the submodule structure of the tensor square of the natural module of the symmetric group over a field of prime characteristic. To do so, we also determine the submodule structure of certain Young modules over a field of characteristic 2. This is joint work with Johannes Orlob.

SS 2011

Dienstag, den 28. Juni 2011, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Dr. Charles Eaton   (School of Mathematics, University of Manchester, (UK))
"Perfect self-isometries of Brauer blocks"

Dienstag, den 21. Juni 2011, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Prof. R. Boltje   (University of California, Santa Cruz, USA)
"Orthogonal units in double Burnside rings"

Dienstag, den 19. April 2011, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Dr. John Murray   (National University of Ireland, Maynooth)
"Combinatorics and Algebras"
Abstract: pdf-Datei

Dienstag, den 22. März 2011, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Prof. Dr. Susumu Ariki   (Osaka University, Osaka, Japan)
"On quasi-hereditary covers of the Hecke algebra of type B₂"
Abstract:Quasi-hereditary covers of the Hecke algebra of type B whose standard objects are labeled by bipartitions attracts some interest because of its relationship with level two Fock spaces. In the first half, I explain the motivation from the level two Fock spaces, and in the second half, I explain examples in rank 2 case.

Dienstag, den 15. März 2011, 14:15 Uhr, SR 3517 Ernst-Abbe-Platz 2

Prof. Dr. Changchang Xi   (Beijing Normal University; China)
"Stable equivalences for perforated Yoneda algebras"
Abstract: pdf-Datei

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