Oberseminar "Lie-Theorie"

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

Programm für das Sommersemester 2011 (April bis September)

Freitag, 15. April 2011; 9:15-10:15 in E2.304

St. Garnier (Metz): Geodesic flow for Riemannian supermanifolds

Abstract: We discuss a notion of geodesics that is different from Goertsches' but in close analogy to the ungraded case. We show that there exists a geodesic flow on the (co-)tangent bundle of the Riemannian supermanifold with the usual basic properties (notably a bijection between "integral curves" of this flow and geodesics).

15./16. April 2011: Topological Groups and Mathematical Physics 7 (Paderborn)

Donnerstag, 21. April 2011; 16:15-17:45 in D1.320

R. Knevel (Bar-Ilan): Verselle Familien von kompakten super Riemannschen Flächen 

Abstract: In meinem Vortrag möchte ich zeigen, wie man verselle Familien kompakter (1,1)-dimensionaler super Riemannscher Flächen konstruiert und zur Konstruktion von Modulräumen solcher Flächen heranzieht. Dabei werde ich insbesondere diskutieren, wieso diese Familien nicht universell sind, ob immer solche versellen Familien existieren, und wie und wo man verselle supersymmetrische Teilfamilien findet. Am Schluss möchte ich einen Ausblick geben über noch offene Fragen und mögliche Verallgemeinerungen in höhere Dimensionen.

J. Hilgert (Paderborn): Das Bild der Impuls-Abbildung

Abstract: In diesem Vortrag wird der Zugang von M. Brion zum Konvexitätssatz von Atiyah-Guillemin-Sternberg erklärt.

M. Laubinger (Paderborn): Laplace-Operatoren in Supergeometrie

Abstract: Wir präsentieren de Bie's Laplace-Operator auf \R^{m|n} und diskutieren seine Fundamentallösung.

Danach definieren wir einen Laplace-Operator auf der Heisenberg-Clifford Lie Supergruppe, und beschreiben, wie dieser als System von partiellen Differentialoperatoren aufgefasst werden kann.

G. Mendoza (Philadelphia): Elliptic operators on manifolds with conical singularities I

Abstract: This is the first of two talks focusing on basic properties of elliptic differential operators on manifolds with conical singularities. In this first lecture I will describe Melrose's approach to elliptic differential operators on manifolds with cylindrical ends, in particular his b-calculus. Parametrices constructed with the b-calculus easily give parametrices for elliptic operators in the case of conical singularities. With these one proves easily fundamental theorems such as the fact that the closed (reasonable) extensions of such operators are always Fredholm operators when the underlying manifold is compact. I will then discuss the structure of the manifold of extensions with emphasis on the case of selfadjoint extensions of symmetric semibounded operators.

G. Mendoza (Philadelphia): Elliptic operators on manifolds with conical singularities II

G. Mendoza (Philadelphia): Zeta functions of elliptic operators on manifolds with conical singularities

Abstract: The spectral $\zeta$ function of an elliptic differential operator (whose principal symbol satisfies a suitable ray condition) has a meromorphic extension to the complex plane with poles contained in a set determined by the dimension of the underlying manifold and the order of the operator. In the case of elliptic operators on manifolds with conical singularities, again with a suitable necessary condition in the principal symbol, this is far from being the case. The $zeta$-function does admit a meromorphic extension to $\mathrm{Re}\,s>0$ with poles in standard locations, but beyond this anything can happen. it is possible for the zeta function of such an operator to admit a meromorphic extension to the rest of the complex plane but with poles in nonstandard locations, or no such extension at all. The underlying reason of this pathology can be traced to phenomena which can be described in geometric terms. After reviewing the classical background on zeta functions of elliptic operators I will give a detailed explanation (based on joint work with J.~Gil and T.~Krainer) on the origin of the pathologies.

Donnerstag, 16. Juni 2011; 16:15-17:45 in D1.320

M.Laubinger (Paderborn): Harmonic analysis on flat superspace

Abstract: We extend our results on the purely odd Heisenberg-Clifford Lie supergroup to the general case. In particular, we define a Fourier transform and a convolution product for superfunctions. The Fourier transform exchanges the convolution and a pointwise product, and is an intertwining operator for the left regular representation. Our work relies on recent results on unitary representations of nilpotent Lie supergroups.

Donnerstag, 30. Juni 2011; 16:15-17:45 in D1.320

M. Kohlmann (Hannover): Modelle für Wasserwellen auf Diffeomorphismengruppen und semidirekten Produkten

K. Rejzner (Hamburg): Applications of the infinite dimensional calculus in the functional approach to classical field theory

Abstract: I will present the formulation of classical field theory, that is based on the notion of smooth functionals on the space of configurations, which is some locally convex vector space. This formalism is motivated by the structures that appear in quantum field theory and allows to understand better the quantization procedure. In my talk I will show, which structures and definitions known from the infinite dimensional differential geometry are important in physics and why are they crucial for our approach.

Ch. Lienau (Hannover):  Temperierte Darstellungen von skalierten Lie-Gruppen und analytische Faktorisierung von nicht unitären Schrödinger-Darstellungen

Abstract: Jede irreduzible Darstellung mit nicht trivialem zentralem Charakter der Heisenberggruppe ist nach dem Satz von Stone und von Neumann äquivalent zu einer unitären Schrödinger-Darstellung. Im Vortrag werden zuerst nicht unitäre Schrödinger-Darstellungen eingeführt. Diese sind, wie ich erläutern werde, Beispiele für temperierte Darstellungen von skalierten Lie-Gruppen. Danach werde ich zeigen, daß die analytischen Vektoren für die nicht unitären Schrödinger-Darstellungen die Faktorisierungseigenschaft besitzen.

 4.-10. September , 2011: JSPS-DFG Seminar Lie Groups: Geometry and Analysis (Paderborn)

Programm früherer Semester 

winter 2010/2011, summer 2010, 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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