Conference talk G. Vegter

G. Vegter
JBI, Groningen
Computational topology for the detection of structure in large data sets

Classification of geometric shapes is one of the central goals of Topology.
The key issue is to find a good notion of equivalence under which this
classification can be carried out in practice, preferably by assigning
discriminating numerical invariants to geometric objects.  The Euler
characteristic is a well known topological invariant of a shape, but in general
it is too weak to distinguish different geometric objects.

Homology theory enriches the topological toolbox with Betti numbers, a whole
sequence of topological invariants of a shape.  Computational Topology provides
fast algorithms for the computation of such numerical invariants, and extensions
thereof.  We explain how these methods work and show that they are useful in
detecting structure in large, possibly noisy, data sets.  The leading cases are
galaxy distributions defining the large scale structure of the universe.

Academy Building
Thursday, April 5, 2012 - 14:00 - 14:50