Explore the concept of magnitude in metric spaces through this 45-minute lecture by Nina Otter. Delve into an isometric invariant introduced by Tom Leinster in 2010 that encodes various properties of metric spaces, including volume, dimension, and capacity. Gain insights into existing results, current research, and the relationship between magnitude and persistent homology. Follow the presentation as it covers topics such as two-point spaces, positive definite matrix bases, compact metric spaces, and related conjectures. Examine examples, open questions, and references to deepen your understanding of this cutting-edge area in applied algebraic topology.
Overview
Syllabus
Introduction
Outline
Magnitude of a metric space
Two point space
Metric space
Positive positive definite matrix bases
Compact metric spaces
Example
Concave magnitude conjecture
Meromorphic magnitude conjecture
Pilot metaclass
Vapors
Open Questions
References
Taught by
Applied Algebraic Topology Network
