The 38th Annual
(Online) Workshop in
The featured speaker is Peter Bubenik of the University of Florida, who will give a series of three one-hour lectures on the Topological Data Analysis. Abstracts can be found below.
The workshop will also feature contributed talks of 20 minutes. Contributed talks need not be directly related to the topic of the principal lectures. If you wish to apply to give a contributed talk please submit a title and abstract on the registration form or send directly to Greg Friedman (send email). It is likely that there will be more volunteers to speak than there are time slots. In that event, the organizers will make the necessary choices in a way that provides a balanced collection of topics and respects the historical traditions of this workshop. Earlier responses may be given some preference. Applicants will be notified whether their talk has been accepted by June 1.
Topological Data Analysis (TDA) uses tools based on topology to address challenges in data science. In these talks I will focus on the part of the subject that uses a parametrized version of homology called persistent homology and emphasize connections to geometry and topology.
In the first talk, I will introduce persistent homology, starting with its origins in the work of Marston Morse. Using geometry, algebra, and combinatorics, we will obtain a summary of the "shape" of data, called the persistence diagram. The collection of these summaries has various metric structures, some of which allow a large assortment of analytic and computational tools to be applied to our topological structures. I will end by showing how TDA can be used to learn the curvature of a surface from the persistent homology of points sampled from the surface.
Lecture 2: Topological Data Analysis - Theory
In the second talk, I will discuss some of the theory of TDA. An important feature of TDA is that many of its constructions have been proven to be stable - errors in the output are bounded by errors in the input. We will see that persistence diagrams and their associated metrics may be obtained by universal constructions. The geometry and topology of these spaces makes their analysis both challenging and interesting. Coarse geometry will help us compare some of these metrics.
Lecture 3: Topological Data Analysis - Multiple Parameters
The final talk will bring us to the multiparameter setting - a topic of great practical interest and a subject of current research. I will discuss why the underlying algebra of the multiparameter case is fundamentally more complicated. Most current computational methods rely on reductions to the single parameter case. I will introduce an approach to multiparameter persistent homology using geometric topology, particularly the generalized Morse theory of Jean Cerf.
Financial support for the workshop series is provided by a grant from the National Science Foundation (DMS-1764311).
Fredric Ancel, University of Wisconsin-Milwaukee
Greg Friedman, Texas Christian University
Craig Guilbault, University of Wisconsin-Milwaukee
Molly Moran, Colorado College
Nathan Sunukjian, Calvin College
Eric Swenson, Brigham Young University
Frederick Tinsley, Colorado College
Gerard Venema, Calvin College
Contact Greg Friedman (send email) if you have questions about the workshop or comments on this web site.