Conference: Summer School "Stability in Topological Data Analysis"

This award provides financial support for junior and early-career US participants in the summer school “Stability in Topological Data Analysis”, to be held at the Institute Mittag-Leffler, Stockholm, Sweden, June 30 - July 4, 2025. Topological Data Analysis (TDA) aims to develop new techniques based on topology and other disciplines in pure mathematics to understand complex data. Research questions are strongly motivated by applications from neuroscience, image recognition, biology, material science, geography, and beyond. The underlying idea is that topology helps recognize patterns within data and, therefore, turn data into compressed, useful knowledge. Besides advancing the progress of science by helping to prepare the next generation of applied topologists, this school is also designed to expand the reach of applied topology. The topic of the school is the study of general techniques to achieve stability of invariants in TDA that can be applied to different objects, from persistence modules to Reeb graphs. In particular, the focus is on questions about the stability of various TDA tools: 1) Which metrics can be introduced to ensure the stability of traditional topological invariants? 2) Which invariants can be developed to ensure stability with respect to traditional metrics? Through questions like these, TDA enriches the traditional fields of algebraic topology and geometry while at the same time striving for theoretical guarantees for practitioners in data analysis. There will be three lecturers alternating in the mornings, an introductory poster section, problem sessions in the afternoons, and a few short research talks from the participants. Ultimately, the school’s goal is to encourage students to develop their own application-motivated results in TDA by considering well-established principled strategies. Further details can be found at: https://www.mittag-leffler.se/activities/ewm-ems-summer-school-stability-in-topological-data-analysis/ This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.