EWM-EMS Summer School: Stability in Topological Data Analysis

June 30 - July 4, 2025

Topological Data Analysis (TDA) aims to develop new techniques based on algebraic topology, commutative algebra, metric geometry, and category theory 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.
The school will focus on questions about the stability of various TDA tools such as persistence modules and Reeb graphs:
  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.
Ultimately, the school’s goal is to encourage students to develop their own application-motivated results in TDA by considering well-established principled strategies.

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