KTH/SU Mathematics Colloquium
06-04-26
Gunnar Carlsson, Stanford University
Algebraic topology and high dimensional data
In recent years techniques have been developed for
evaluating Betti numbers of spaces given only a finite but large set
of points (a "point cloud") sampled from the space. Such techniques
can be applied in statistical settings where the data being
considered is high dimensional (and hence cannot be visualized) and
non-linear in nature. This talk will describe the techniques
required to obtain the Betti numbers, as well as discuss some actual
examples where they have been applied.