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This course aims to teach learners about the magnitude of a metric space, an isometric invariant that encodes various properties of metric spaces such as volume, dimension, and capacity. The course covers topics such as two-point space, positive definite matrix bases, compact metric spaces, concave magnitude conjecture, and meromorphic magnitude conjecture. The teaching method involves providing an overview of existing results, current research, and the relationship between magnitude and persistent homology. This course is intended for individuals interested in advanced topics in mathematics and algebraic topology.
