The magnitude of a metric space

Tuesday, February 2, 2016 - 2:00pm
Math Sci 111
Mark Meckes
(Case Western Reserve University)

Magnitude is an invariant of metric spaces introduced by Leinster,
motivated by considerations from category theory.  Although its
definition is abstract and algebraic, in Euclidean space magnitude
rather surprisingly turns out to be closely related to classical
geometric quantities, like volume and dimension, and its computation
involves harmonic analysis and partial differential equations.  I will
discuss where magnitude comes from, how these surprising connections
arise, what we know, and what we don't know about magnitude.

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