Title: Global Methods for High-dimensional datasets

                 Herbert Edelsbrunner
  		Arts and Sciences Professor of 
		Computer Science and Mathematics
			Duke University

ABSTRACT: Considering the problem of learning about the structure
  of large and possible high-dimensional datasets, we take a
  global approach aiming at determining their gross topology.
  Specifically, we introduce a parametrized family of witness
  complexes modeling the data and methods to extract the stable,
  or persistent topology from the family.
         
  On April 7th, we introduce geometric complexes (Cech, Rips,
  Alpha, and almost Alpha complexes) and the corresponding witness
  complexes used to model the datasets.  A key result in this
  context is the Weak Delaunay Theorem by de Silva, which we
  generalize from Delaunay to almost Alpha complexes.

  On April 14th, we will model the alpha-beta witness complexes
  after the family of almost Alpha complexes. We also will
  introduce the concept of persistent homology and use it to
  extract the 'stable' topology of the modeled datasets.