Claudia Landi: Computational topology and shape comparison

In the last twenty years, computational topology has contributed with a number of methods to deal with the task of describing and comparing shapes. The ultimate goal of this research area is to provide topological  ground for classification and retrieval of digital shapes contained in a database based on content. The general pipeline in this field is to associate with each shape a shape descriptor and then recast the shape comparison problem as a metric problem on shape descriptors. The talk will report on the state of the art of some popular topological shape descriptors coming from the Persistent Homology Theory. In particular,  persistence diagrams with the bottleneck distance and persistence modules with the interleaving distance will be reviewed  and shown to satisfy stability and optimality properties.