Jürgen Jost - Geometry and Topology of Data

Explore the intersection of geometry and topology in data analysis through this 50-minute lecture by Jürgen Jost. Delve into the fundamental differences between topological and geometric approaches to data analysis, focusing on the concept of curvature and its relationship to convexity. Learn about weighted circumcenters, hyper convex spaces, and gamma hyperbolic spaces. Gain insights into how these mathematical concepts can be applied to analyze complex datasets. Engage with thought-provoking questions and speculative ideas presented throughout the talk, enhancing your understanding of advanced data analysis techniques.

Introduction
Geometry and Topology
Notation
Reformulation
Weighted circumcenters
General definition
Examples
Hyper convex spaces
Hyper convex variants
Curvature
Conclusions
Questions
Gamma hyperbolic spaces
More than 3 points
Topology
Speculative Question
Final Question