Oberseminar "Lie-Theorie"

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 Das Oberseminar findet üblicherweise donnerstags 16-18 Uhr in D1.320 statt.

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Programm für das Sommersemester 2010 (April bis September)

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Seminar Sophus Lie,  Mulhouse (April 22-24, 2010)

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Donnerstag, 29. April 2010; 16:15-17:45 in E2.304

O. Goertsches (Köln): Riemannsche Metriken auf Liesupergruppen und homogenen Superräumen

Abstract: We will introduce graded versions of (left- and bi-, respectively G-)invariant metrics on Lie supergroups and homogeneous superspaces. Elementary facts almost trivial to prove in the usual setting, like the correspondence between biinvariant metrics on a Lie group and Ad-invariant scalar products on the Lie algebra, still hold but their proof becomes more involved. After pointing out some of these difficulties we will give a definition of Riemannian symmetric superspaces and some examples.

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Freitag, 30. April 2010; 14:15-15:45 in E2.316

B. Schwartz (Marburg): Jordan theory and the fine structure of generalized flag manifolds

Abstract: The purpose of this talk is to introduce some notions of Jordan theory and to present some of its applications to complex geometry. We review the classification of hermitian symmetric spaces via Jordan theory, and describe the Jordan theoretic model of the compact dual X of a non-compact hermitian symmetric space G/K due to O. Loos. Using this model, a detailed description of the G-orbits of X and their Matsuki-duals can be given. In the second part of the talk we extend Loos' construction to more general complex flag manifolds and indicate some of its applications.

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Donnerstag, 20. Mai 2010; 16:15-17:45 in D1.320

U. Ray (Reims): On Cartan subalgebras

Abstract: Cartan subalgebras play a fundamental role in finite dimensional Lie algebra theory. In this talk, I will discuss the feasibility and usefulness of generalizing the notion of a Cartan subalgebra to a Lie algebra of infinite dimension, in particular to the class of locally reductive or more generally locally finite Lie algebras and that of Borcherds-Kac-Moody algebras.

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Transformation Groups and Mathematical Physics

May 28-29, 2010, Research II Lecture hall at Jacobs University Bremen

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Donnerstag, 17. Juni 2010; 16:15-17:45 in D1.320

H. Salmasian (Ottawa): Unitary representations of nilpotent super Lie groups

Abstract: In the 1950's Kirillov established a correspondence between coadjoint orbits and irreducible unitary representations for nilpotent Lie groups. Kirillov's classical work is a prototypical example of the orbit method philosophy in the theory of representations of Lie groups. I this talk, I begin by introducing the orbit method philosophy and explaining Kirillov's work. Then I define Lie supergroups and their unitary representations. Finally I prove a result analogous to Kirillov's for nilpotent Lie supergroups. The final result is somewhat surprising, in that it shows that the supergroup has fewer representations than its even part.

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Donnerstag, 2. September 2010; 16:15-17:45 in D1.320

I. Roy (Metz/Paderborn): Foliated rho-invariants and their stability properties

Abstract: In the first part of this talk we will introduce foliated rho-invariants on measured foliations and state some of their stability properties. In the second part, we will give an extension of the formalism of Hilbert-Poincaré(HP) complexes to the case of foliations and give an explicit homotopy equivalence of HP-complexes on leafwise homotopy equivalent foliations. Finally, we shall give an application of this formalism for partially extending the proof of the homotopy invariance of the classical Cheeger-Gromov rho-invariant to the foliated case.

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Program of previous semesters

winter 2009/2010, summer 2009, winter 2008/2009 , summer 2008 , winter 2007/2008, summer 2007 , winter 2006/2007, summer 2006, winter 2005/2006, summer 2005, winter 2004/2005, summer 2004

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Fragen, Bemerkungen und Vorschläge bitte an Joachim Hilgert

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Impressum | Webmaster | Letzte Änderungen am: 26.03.2010

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