# Jerusalem Mathematics Colloquium

Thursday, 7th April 2005, 4:00 pm

Mathematics Building, Lecture Hall 2

We are proud to host a lecture in the
Landau Center Anniversary Symposium.
##

Matthias Kreck

(Heidelberg University)

"What is typical: symmetric or asymmetric manifolds"

** Abstract: **

For a metric space a symmetry is an isometry of the space.
Geometrically the most interesting spaces are Riemannian manifolds.
Although most Riemannian manifolds which occur "in nature" admit
non-trivial symmetries, one expects that this is not typical. A much
stronger expectation was formulated about 30 years ago by Raymond and
Schulz, namely that a compact smooth manifold picked at random is
asymmetric, meaning that for all Riemannian metrics the group of
isometries is trivial. I would like to report on the state of the art.

Until recently the only known examples of asymmetric manifolds were
certain aspherical manifolds, where one uses the fundamental group to
show that these manifolds are asymmetric. I want to report about new
results concerning simply connected manifolds.

Light refreshments will be served at 3:30.

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