Applied homological algebra beyond persistence diagrams

June 19 to June 23, 2023

at the

American Institute of Mathematics, San Jose, California

organized by

Chad Giusti, Gregory Henselman-Petrusek, and Lori Ziegelmeier

Original Announcement

This workshop will bring together theorists and computationalists to collaborate on understanding how computational considerations impact the practice of applied topology, and what new challenges for computation we must solve to bridge theory to applications.

Much of the existing work in topological data analysis relies on the use of persistence diagrams as a feature set for complex data. However, applied topology has the potential to provide much more detailed information about and explicit connections among complex data sets, providing quantitative methods for characterizing and investigating structure in data that go beyond classification or regression. Building these methods will require the efforts of experts in the theory of algebraic and geometric topology, who can adapt existing tools or develop novel approaches inspired by the applications. However, for these new methods to be useful outside of the domain of pure mathematics, they need to be instantiated as software.

Potential Topics:

Topological models of complex systems: vector bundles, spaces with group actions, etc.
Effective data structures and algorithms for topological and algebraic objects.
Algebraic structures: cup products, maps on (persistent) homology, etc.
Cycle representatives, geometry, and other in situ interpretation of homology classes.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.