# Minicourses

**The minicourses will be accessible for graduate students. All the lectures will include sketches of open problems, offering entry points into the theory for young researchers.**

## Analysis on Homogeneous Spaces

### Toshiyuki Kobayashi (University of Tokyo)

At the foundation of harmonic analysis are the well-known principles that a geometric space may be studied though its space of functions, and that the analysis of these functions is simplified by taking into account the symmetries of the space.

Over the past 60 years, considerable developments have occurred in the global analysis on spaces acted upon by real reductive groups as a generalization of Fourier analysis.

These lectures will focus on several fundamental aspects of this study in which irreducible tempered representations act as “building blocks” of Langlands’ classification theory. Topics will include: real spherical manifolds, the representation theory of real reductive groups, branching laws, tempered homogeneous spaces, examples and applications of tempered varieties.

## C*-Algebras, K-Theory and Tempered Representations

### Nigel Higson (Penn State)

C*-algebra theory owes its beginnings to the unitary representation theory of locally compact groups. With the growing interest in more conceptual and more geometric views in representation theory, and the rapid development of geometric tools in C*-algebra theory, the two subjects are drawing closer together once again, to their mutual advantage.

These lectures will trace some of these recent developments from the C*-algebra point of view, starting with a short discussion of basic ideas in C*-algebra theory and their relevance to representation theory, moving on to K-theory and the Connes-Kasparov isomorphism, and from there to the Mackey bijection. A final lecture will consider prospects for the further development of the C*-algebra / representation theory interaction.