for this workshop
Applied homological algebra beyond persistence diagrams
American Institute of Mathematics, San Jose, California
Chad Giusti, Gregory Henselman-Petrusek, and Lori Ziegelmeier
This workshop, sponsored by AIM and the NSF, 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.
- 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.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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