Oberseminar "Lie-Theorie"

 Das Oberseminar findet üblicherweise donnerstags 16-18 Uhr in A2.337 statt. 

Nächster Vortrag: 

Donnerstag, 2. Februar 2012; 16:15 - 17:45 in A2.337
 

B. Camus (Bochum): Semi-classical trace formulae and applications

Programm für das Wintersemester 2011/2012 (Oktober bis April)

Donnerstag, 20. Oktober 2011; 16:15-17:15 in A2.337

S. Hansen (Paderborn): Helgason's conjecture

Abstract: Around 1970 Helgason conjectured a general Poisson integral representation of the joint eigenfunctions of the invariant differential operators on symmetric spaces. In a 1978 Annals paper this conjecture was resolved positively by Kashiwara, Kowata, Minemura, Okamoto, Oshima, and Tanaka. We give an introduction to the conjecture and its solution.

Donnerstag, 27. Oktober 2011; 16:15-17:15 in A2.337

B. Schwarz (Paderborn): Spherical representations on symmetric R-spaces

Abstract: Let X=U/K be a compact Riemannian symmetric space. The Cartan-Helgason Theorem gives a details description of the decomposition of the L^2-space on X into irreducible U-modules, the so called spherical representations of U. By compactness, all these U-modules are finite dimensional, and Borel-Weil Theory provides a (rather abstract) geometric realization of each of them as the space of holomorphic sections in a line bundle over some complex projective variety. The aim of this talk is to provide an explicit description of this geometric realization in the case of symmetric R-spaces, i.e. compact Riemannian symmetric spaces that admit a Jordan theoretic description. We discuss the hermitian case in detail and indicate how to handle the real case by imbedding real symmetric R-spaces into their complexifications.

Donnerstag, 3. November 2011; 16:15-17:15 in A2.337

T. Pecher (Paderborn): Multiplicity-free actions and dual pairs

Abstract: A basic question in representation theory is, given a module V of a reductive group G, to determine its decomposition into irreducibles. Special cases of interest are the tensor product problem, or branching rules. In general, V is called multiplicity-free if dim Hom(V,W) ≤ 1 for all irreducible G modules W. Decompositions of that type often give rise to further results in other situations. 

In this talk, we show the importance of the multiplicity-freeness condition for V being a supersymmetric power of a G-module. These actions have some interesting properties. For example, their algebra of G-invariant polynomial differential operators has a very special structure. In particular, it has a canonical basis which leads to Capelli-type identities. Furthermore, some results of classical invariant theory can be proven by means of multiplicity-free (super-)symmetric algebras. In the second part of the talk, we shall sketch the classification of those modules and show how this can be achieved by means of Howe´s dual pairs. 

Freitag, 18. November 2011; 9:00 - 12:30 in Paderborn in C 4.208

Zusammen mit der Arbeitsgruppe von B. Krötz (Hannover) soll in diesem Semester die Arbeit "Effective equidistribtion for closed orbits of semisimple groups on homogeneous spaces" von M. Einsiedler, G. Margulis und A. Venkatesh (Invent. math (2009) 177: 137--212), besprochen werden. 

B. Krötz (Hannover): Invariance of measures on homogeneous spaces (§2)

M. Güngor (Hannover): Adeles 

J. Hilgert (Paderborn): Boundary value maps and differential systems with regular singularities

Freitag, 9. Dezember 2011; 9:00 - 12:30 in H7
 

J. Hilgert (Paderborn): Effective equidistribution (Invent. math (2009) 177: 137--212, §4)

Ch. Lienau (Hannover): Automorphic forms, classical vs. adelic point of view 

Donnerstag, 15. Dezember 2011; 16:15-17:15 in A2.337

B. Schwarz / H. Seppänen (Paderborn): Symplectic branching laws and Hermitian symmetric spaces I

Mittwoch, 21. Dezember 2011; 11:00-12:00 in O1.224

B. Schwarz (Paderborn): Symplectic branching laws and Hermitian symmetric spaces II

Donnerstag, 5. Januar 2012; 16:15-17:15 in A2.337

J. Hilgert (Paderborn): Radial components and regular singularities for symmetric spaces

Donnerstag, 19. Januar 2012; 15:00 - 18:30 in B1 / A2.337
 

B. Schwarz (Paderborn): Hyperfunctions (B1)

J. Hilgert (Paderborn): Boundary value maps and differential systems with regular singularities II (A2.337)

Freitag, 20. Januar 2012; 9:00 - 12:30 in D1.338
 

B. Krötz (Hannover): Applications of effective equidistribution (Invent. math (2009) 177: 137--212, §17)

Ch. Lienau (Hannover): Tate's thesis 

Donnerstag, 26. Januar 2012; 16:15-17:15 in A2.337

A. Pohl (Zürich): Escape of mass and entropy for diagonal flows

Abstract: It is well-known that on compact spaces, metric entropy is upper semi-continuous and mass cannot escape. On non-compact spaces the situation changes drastically. Given any homogeneous space of the form L\G, where G is any connected semisimple Lie group of real rank one with finite center and L a non-cocompact lattice in G, we will discuss a relationship between the metric entropy of homogeneous diagonal flows on L\G and escape of mass. This is joint work with Manfred Einsiedler and Shirali Kadyrov.

Donnerstag, 2. Februar 2012; 16:15-17:15 in A2.337

B. Camus (Bochum): Semi-classical trace formulae and applications

Abstract: In this talk I will discuss the semi-classical trace formula. This formula relates:

- the asymptotic behavior of the spectrum of a quantum operator.

9.-11. Februar: Seminar Sophus Lie (Reims)

Programm früherer Semester

summer 2011, 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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