Mon, May 7, 2007; 5:15 pm in E2.304

J. Sauter (Paderborn): On Hodge numbers of p*-trivial vector bundles

Abstract:

We consider a Galois covering p of complex smooth projective varieties. The category of p*-trivial vector bundles is equivalent to the category of complex representations of the decktransformation group G. A field automorphism of the complex numbers induces a group automorphism of GL_n(C). If we compose a repesentation of G with such a group homomorphism, we show that the Hodge numbers of the two corresponding vector bundles are the same. This talk is on my diploma thesis.

Fri, May 11, 2007; 2:15 pm in D1.320

G. Link (Karlsruhe/Zürich): Schottky groups in higher rank symmetric spaces

Abstract:

In this talk I will describe a certain type of free groups, so-called Schottky groups, acting by isometries on a globally symmetric space X of non compact type and higher rank. In particular, I am interested in the asymptotic growth rate of the number of primitve closed geodesics of period less than T (modulo free homotopy) in the quotient. I will explain a geometric idea of the proof that this growth rate is equal to the critical exponent of the Schottky group.

Mon, May 14, 2007; 5:15 pm in E2.304

M. Lindström (Abo): Schröder's  equation and eigenvalues

Abstract:

In this talk we consider Schröder's functional equation f o β = γ f. Here β is the given quantity, a holomorphic selfmap of the unit disc D in the complex plane C, and the goal is to find γ in C and f holomorphic on D so that f o β = γ f. Thus Schröder's equation is the eigenvalue equation for the composition operator C_β, defined by C_β(f)= f o β, where f is holomorphic on D. We discuss solutions in various function spaces.

Mon, May 21, 2007; 5:15 pm in E2.304

St. Wolf (Paderborn): The composition monoid over different fields

Abstract:

Reineke introduced a multiplicative structure on closed irreducible
sets in the representation variety of quivers. He called this the generic
extension monoid. One can restrict the interest to the submonoid generated by
the simple representations. The elements are \mathbb{Z}-schemes, therefore it
makes sense to talk about base change of the monoid. In this talk I will show
that, if the quiver is tame, for each algebraically closed field the
corresponding composition monoids are isomorphic. Moreover I will give some
relations between the composition monoids and Hall algebras.

IRTG-Minicourse in Paderborn

A. Pasquale (Metz): Cherednik Operators and Hecke Algebras

Wed, May 23,  12:15 am - 1:45 pm in C3.232

Thu, May 24,  1:00 pm - 2:00 pm in D1.312

Fr, May 25,  1:15 pm - 2:45 pm in C3.232

Tue, May 29,  1:00 pm - 2:00 pm in D1.320

Wed, May 30,  12:15 am - 1:45 pm in A2

Thu, May 31,  1:00 pm - 2:00 pm in D1.312

Fr, June  1,  1:15 pm - 2:45 pm in C3.232

PROGRAM

Mon, June 11, 2007; 5:15 pm in E2.304

J. Hilgert (Paderborn): Transfer operators, Hankel transforms, and holomorphic discrete series representations

Abstract:

We report on some joint work in progress with D. Mayer on a Hilbert space setting for transfer operators and their meromorphic continuations.

Mon, June 18, 2007; 5:15 pm in E2.304

N. Dichev (Paderborn): Thick subcategories of quiver representations

Abstract:

For a finite and acyclic quiver Q denote by repQ the category of finite dimensional kQ-modules. Define thick subcategories of repQ to be exact abelian subcategories of repQ closed under extensions. The
importance of thick subcategories is highlighted by Ingalls and Thomas' paper "Noncrossing partitions and representations of quivers", where they have established bijections between finitely generated thick
subcategories, finitely generated torsion classes, support tilting modules (all in repQ) and cluster tilting objects in the cluster categories. In my talk I will focus on relations between thick subcategories, perpendicular categories and exceptional sequences as well as some other aspects of Ingalls and Thomas' paper. The lattice structure of thick subcategories when Q is a Dynkin quiver will be discussed.

Mon, June 25, 2007; 5:15 pm in E2.304

W. van der Kallen (Utrecht): First fundamental theorem of invariant theory, algebraic group cohomology, and geometry

Abstract:

We recall some invariant theory, explain our conjectural cohomological generalization and discuss how algebraic geometry of flag varieties and Grassmannians helps studying such issues.

Mon, July 2, 2007; 5:15 pm in E2.304

A. Alldridge (Paderborn): Combinatorial Equivalence of Polytopes and the Index of
Wiener-Hopf Operators

Abstract:

Let P be a d-dimensional convex polytope. We may consider the (d+1)-dimensional convex cone C whose section is P and the associated C*-algebra A of Wiener-Hopf operators. Then we prove that the Morita equivalence class of A is a complete invariant for the combinatorial type of P.

In fact, by previous work of T. Johansen and the speaker, A is a type I C*-algebra of finite length. The composition series of A induces Atiyah-Hirzebruch type spectral sequence in K-theory. In the particular case considered here, the KK-theoretical index theorem of T. Johansen
and the speaker can be evaluated geometrically. As a consequence, the spectral sequence abuts to its E_2 term, and its E_1 term turns out to be precisely the cellular complex of P.

Moreover, A is KK-contractible (in particular, has trivial K-theory), and A/K (where K=compact operators) is KK-equivalent to K where, on level of K-theory, the equivalence is given by the (integer) index of Fredholm matrices of Wiener-Hopf operators.

July 20-24, 2007 in Bielefeld

Joint meeting of

"Algebraic Groups, Lie Groups and Transformation Groups"

and

"Seminar Sophus Lie"

organized in honor of E.B. Vinberg's 70th birthday

Program

Fri, August 10, 2007; 3:15 pm in A6

D. Pronk (Halifax): Groupoid Representations for Orbifolds

Abstract:

Smooth orbifolds can be represented by proper etale Lie groupoids. However, this representation
is only unique up to essential equivalence of groupoids. We will discuss what this means for the description of maps between orbifolds in terms of groupoid homomorphisms. One can take isomorphism classes of maps and obtain a category of fractions, which can be described using Hilsum-Skandalis maps. However, we will choose a 2-categorical approach where we will
keep explicitly track of the isomorphisms between the morphisms. This way we obtain a description of the category of orbifolds as a bicategory of fractions of the category of orbifold groupoids with respect to the class of essential equivalences. This bicategory gives us the right notion for the fibered product of orbifolds as used for example by Thurston in his construction of the universal covering orbifold.

As an application of this construction we will consider the category of representable orbifolds and give an explicit description of maps between such orbifolds in terms of equivariant maps between translation
groupoids. This description can be used to define orbifold Bredon cohomology.

Mon, August 13, 2007; 10:00 am in D1.328

S. Trivedi (Chennai): Simplicial Complexes Associated to a Relation - A Theorem of Dowker (45 Min)

Mon, August 13, 2007; 11:00 am in D1.328

M. Schröder (Paderborn): Propagation of Singularities (45 Min)

J.L. Tu (Metz): Wrong-way functoriality in twisted K-theory