The magnitude of a metric space
Tom Leinster (Glasgow)
Tuesday 24th November, 2009 16:00-17:00 214
Magnitude is a numerical invariant of metric spaces with its origins in category theory. It seems to be new to mathematics, although it has made sporadic appearances in the literature on biodiversity. In principle it is only defined for finite spaces. But thanks to a recent group effort (involving some Fourier analysis and some members of this department), we now know that there is a decent definition of magnitude for compact subsets of R^n. And the evidence - both numerical and analytic - suggests that this single invariant encapsulates all the most important invariants of geometric measure theory. I will explain all this. No specialist knowledge of anything will be assumed.