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Tee-Seminar der AG KramerZeit und Ort:
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Inhalt:
Mitglieder der Arbeitsgruppe und Gäste tragen über ihre laufenden Forschungsarbeiten vor, oder über Themen, die uns interessieren. Vor dem Seminar (ab 10:00) gibt es in Zimmer 301b Tee.
Vorträge:
21.04.15
Antoine Beljean (Münster), The Leray-Serre Spectral Sequence adapted to Euclidean Buildings
Abstract : The Leray-Serre spectral sequence is a powerfull tool of algebraic topology that one can apply to fibrations. It enables one to express the (co-)homology of the total space in terms of the co-homologies of the base space and of the fiber. The essential ingredient to construct this spectral sequence in the case of a fibration is its homotopy-lifting property.
We propose in this talk to modify the situation : take a Euclidean building as the base space, its direction bundle (which is the union of the spaces of directions of all points in the building, equiped with a nice topology) as the total space, and the space of directions over a point as the fiber over this point. Can one build a spectral-sequence which expresses relations between the homologies of these spaces ? Since the homotopy-lifting property is no longer available to construct the spectral sequence, we propose to do it using other nice properties of Euclidean buildings.
28.04.15 Nils Leder (Münster), Homological stability of Coxeter groups
02.06.15 Jeroen Schillewaert (Münster), Metrical completeness in Bruhat-Tits buildings
09.06.15
Adam Thomas (Cambridge), The Jacobson-Morozov Theorem and Complete Reduciblity of Lie subalgebras
Abstract: The well-known Jacobson-Morozov Theorem states that every nilpotent element of a complex semisimple Lie algebra $\mathfrak{g} = Lie(G)$ can be embedded in an $\mathfrak{sl}_2$-subalgebra, and a result of Kostant says this can be done in a unique way, up to conjugacy by $G$. Much work has been done on extending this fundamental result to the modular case when $G$ is a reductive algebraic group over an algebraically closed field of characteristic $p > 0$. I will discuss recent joint work with David Stewart, proving that the above result holds in the modular case precisely when $p$ is larger than $h(G)$, the Coxeter number of $G$. In doing so, we consider complete reduciblilty of subalgebras of $\mathfrak{g}$ in the sense of Serre/McNinch. For example, we prove that every $\mathfrak{sl}_2$-subalgebra of $\mathfrak{g}$ is completely reducible precisely when $ p > h(G)$.
23.06.15 Olga Varghese (Münster), Actions of SAut(F_n) on manifolds
!!! 2 Talks on July 21st !!! :
21.07.15 10H30 in SR1C Cora Welsch (Münster), Untergruppen von Gruppen mit Präsentierung
21.07.15 13H00 in SR1C Nils Leder (Münster) und Olga Varghese (Münster), Übersetzung von Kazhdan's Eigenschaft (T) in die geometrische Gruppentheorie