MATERIALS    

In this workshop, we investigate the topology of homeomorphism and diffeomorphism groups of manifolds. Given a topological fibre bundle of smooth manifolds, we ask if the bundle admits differentiable structures, and how many different such structures exist. To this end, we will introduce and study Riemann-Roch theorems for flat vector bundles and different versions of torsion invariants for families of smooth manifolds. There are three major approaches to this topic, based on algebraic K-theory, Morse theory and on heat kernels.

The workshops aims to give concise introductions to the different flavors of higher torsion invariants for smooth fiber bundles, and cumilate in some of the important applications. It is aimed at Graduate Students who want to learn about this interesting subject, and also on experts in one of the fields, who want to learn more about the complementary approaches and the connections between them.

The workshop will lead to the point where one can follow the talks of the miniconference about recent and ongoing research about higher torsion and related questions.

It consists of four interdependend courses: PROGRAM (tentative)

Kiyoshi Igusa (Brandeis):	A∞ functors and higher Franz-Reidemeister torsion
Michael Weiss (Aberdeen):	An index theory without operators
Bruce Williams (Notre Dame):	Reidemeister torsion via Riemann Roch
Sebastian Goette (Regensburg):	Analytic torsion for families

The following miniconference will consists of about ten lectures about current results and ongoing research in the different areas dealing with higher torsion invariants and applications.

Confirmed speakers of this miniconference include: W. Doriabiala, J. Heitsch, K. Igusa, J.R. Klein, K. Koehler, X. Ma, M. Weiss, B. Williams

Lectures start Monday afternoon, the workshop will end Friday before noon. The mini-conference will start Friday afternoon and end sunday at noon.

Organizers:

Ulrich Bunke (Göttingen)
Sebastian Goette (Regensburg)
Thomas Schick (Göttingen)

For further questions and to register please contact one of the organizers.

The workshop is funded in part by the GK "Gruppen and Geometrie", Göttingen and in part by the DFG-program "Global differential geometry". Limited funds are available for participants, in particular for PhD. students and recent graduates.