Lectures and Colloquia during the semester

** November 5, 2001**

Technische Universität Berlin

Straße des 17. Juni 136, 10623 Berlin

Math building - Room MA 042
- map -

** Lecture - 14:15**

### Jiri Matousek -

### Weak epsilon-nets for convex sets

*Abstract: *
Let *X* be a finite set in the *d*-dimensional Euclidean space.
A set *N* is called weak epsilon-net for *X* (with respect to convex sets)
if every convex set containing at least epsilon.*|X|* points of *X*
intersect *N*. Existence results and applications will be
discussed, as well as some related open problems.

** Colloquium - 16:00**

### Frank Lutz - Technische Universität Berlin

### How to Recognize the Topological Type of a Manifold?

*Abstract: *
It was shown by A.A. Markov in 1958 that the homeomorphism
problem for manifolds is unsolvable in dimensions *d \geq 4*,
i.e., there is no algorithm to decide whether two given
manifolds *M^d* and *N^d* are homeomorphic or not.
Still worse, S.P. Novikov proved that even the standard sphere *S^d*
is not recognizable algorithmically when *d \geq 5*.

Despite of these results, there is a number of procedures and
heuristics which, at least in special cases and situations,
allow to recognize the topological type of particular manifolds.
In this talk, we will survey such methods from a "practical point
of view".

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