We will give a summary of the topological methods for understanding complex data sets. We will discuss the persistent homology theme as well as the theme which deals with geometric representations of data.
Creator:
Carlsson, Gunnar (Stanford University)
Created:
2013-10-07
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
I would like to talk about the interaction of traditional algebraic topology and homotopy theory with applied topology, and specifically describe specifically some opportunities for better integration of "higher tech" techniques into applications.
Creator:
Carlsson, Gunnar (Stanford University)
Created:
2022-08-05
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
Over the last ten years, a number of methodologies have been developed which leverage topological techniques and ways of thinking to provide understanding of point cloud data. These include ways of 'measuring' shape via homological signatures, topological mapping techniques, and applications of certain kinds of diagram constructions to collectio...
Creator:
Carlsson, Gunnar (Stanford University)
Created:
2012-03-26
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
The nature and quantity of data arising out of scientific applications requires novel methods, both for exploratory analysis as well as analysis of significance and validation. One set of new methods relies on ideas and methods from topology. The study of data sets requires an extension of standard methods, which we refer to as persistent topolo...
Creator:
Carlsson, Gunnar (Stanford University)
Created:
2008-10-29
Contributed By:
University of Minnesota, Institute for Mathematics and its Applications.
