Introduction

This volume represents the proceedings of the conference in honor of Henri

Moscovici held in Bonn, June 29 – July 4, 2009. Moscovici has made fundamental

contributions to Noncommutative Geometry, Global Analysis and Representation

Theory. Especially, his 30-year long collaboration with A. Connes has led to a num-

ber of foundational results. They obtained an L2-index theorem for homogeneous

spaces of general Lie groups, generalizing the Atiyah-Schmid theorem for semisim-

ple Lie groups and a higher index theorem for multiply connected manifolds. The

latter played a key role in their proof of the Novikov conjecture for word-hyperbolic

groups. In the course of their work on the transverse geometry of foliations they

discovered the local index formula for spectral triples. The calculations based on the

latter formula provided the impetus for the development of the cyclic cohomology

theory of Hopf algebras.

In the words of Alain Connes: “I have always known Henri as a prince who

escaped from the dark days of the communist era in Romania. With his Mediter-

ranean charm and his intense intelligence, so often foresighted, but never taking

himself too seriously, with his inimitable wit, and his constant regard for others he

certainly stands out among mathematicians as a great and lovable exception.”

The present volume, which includes articles by leading experts in the ﬁelds

mentioned above, provides a panoramic view of the interactions of noncommutative

geometry with a variety of areas of mathematics. It contains several surveys as well

as high quality research papers. In particular, it focuses on the following themes:

geometry, analysis and topology of manifolds and singular spaces, index theory,

group representation theory, connections between noncommutative geometry and

number theory and arithmetic geometry, Hopf algebras and their cyclic cohomology.

We now give brief summaries of the papers appearing in this volume.

1. D. Barbasch and P. Pandˇ zi´ c “Dirac cohomology, unipotent representa-

tions.”

In this paper the authors study the problem of classifying unitary repre-

sentations with Dirac cohomology, focusing on the case when the group G is

a complex group viewed as a real group. They conjecture precise conditions

under which a unitary representation has nonzero Dirac cohomology and show

that it is suﬃcient.

2. P. Bressler, A. Gorokhovsky, R. Nest and B. Tsygan “Algebraic index the-

orem for symplectic deformations of gerbes.”

Gerbes and twisted diﬀerential operators play an increasingly important

role in global analysis. In this paper the authors continue their study of the

algebraic analogues of the algebra of twisted symbols, namely of the formal

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