INTENSIVE LECTURES in TOPOLOGICAL DATA ANALYSIS

Prof. Gunnar E. Carlsson

Anne & Bill Swindells Professor
Department of Mathematics
School of Humanities and Sciences
Stanford University

(1) Title: Persistent Homology

Location: 3/25/2014 (Tue) 2pm Sangsan 101

Abstract: Homology is a method for assigning signatures to geometric objects which reflects the presence of various kinds of features, such as connected components, loops, spheres, surfaces, etc. within the object. Persistent homology is a methodology devised over the last 10-15 years which extend the methods of homology to samples from geometric objects, or point clouds. We will discuss homology in its idealized form, as well as persistent homology, with examples.

(2) Title: Structures on Persistence Barcodes and Generalized Persistence.

Location : 3/25/2014 (Tue) 4pm Sangsan 101

Abstract: Persistent homology produces invariants which take the form of barcodes, or finite collections of intervals. There are various structures one can imposed on them to yield a useful organization of the space of all barcodes. In addition, there are generalized forms of persistence, including multidimensional persistence and zig-zag persistence. We will discuss all these aspects of the theory.

(3) Title: Topological Mapping of Point Cloud Data

Location : 3/26/2014 (Wed) 4pm Sangsan 101

Abstract: One of the important problems in understanding large and complex data sets is how to provide useful representations of a data set. We will discuss some existing methods, as well as topological mapping methods which use simplicial complexes as the representation, with examples.