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Venue
Topology
seminar, University
of Aberdeen, 27 October 2014.
Abstract This talk is part of a large programme to define and investigate cardinality-like invariants for a wide range of mathematical objects, from categories to metric spaces to probability distributions to associative algebras. When the general method is applied to graphs, what comes out is a graph invariant — "magnitude" — that can expressed as either a rational function or a power series over Z. It appears to contain quite different information from classical graph invariants; for instance, it is not a specialization of the Tutte polynomial. Moreover, Richard Hepworth has recently found a categorification of graph magnitude, defining a homology theory of which magnitude is the Euler characteristic. I will explain, assuming not much knowledge of anything (and certainly none of graph theory). Slides In this pdf file. Related arXiv:1401.4623, and these discussions (1, 2, 3).
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