Logic Seminar, University of
Manchester, 14 May 2009.
Abstract Notions of size are central to mathematics. From a tender age, we learn to count apples and measure with a ruler. Later we may learn more advanced notions of size: the dimension of a vector space, the Euler characteristic of a topological space, the entropy of a probability space, the biodiversity of an ecosystem, and so on. I will explain the common threads running through these and other notions of size. As an illustration of the helpfulness of this general point of view, I will explain how it led to a new and apparently profound notion of the size of a metric space.
No special knowledge of anything will be assumed.
Slides Slides covering about the first two-thirds of the talk are in this pdf file (1.4MB). (The last third was on the blackboard.)