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CATEGORIES:Mathematics Colloquium
SUMMARY:The many faces of magnitude - Tom Leinster (Edinbu
rgh)
DTSTART:20141203T160000Z
DTEND:20141203T170000Z
UID:TALK1543AT
URL:/talk/index/1543
DESCRIPTION:The magnitude of a square matrix is the sum of all
the entries of its inverse. This strange definit
ion\, suitably used\, produces a family of invaria
nts in different contexts across mathematics. All
of them can be loosely understood as "size". For
example\, the magnitude of a convex set is an inv
ariant from which one can conjecturally recover ma
ny important geometric measures: volume\, surface
area\, perimeter\, and so on. The magnitude of a
graph is a new invariant that shares features with
the Tutte polynomial but is not a specialization
of it. The magnitude of a category is very closel
y related to the Euler characteristic of a topolog
ical space. Magnitude also appears in the difficu
lt problem of quantifying biological diversity: un
der certain circumstances\, the greatest possible
diversity of an ecosystem is exactly its magnitude
. I will give an aerial view of this landscape.\n
LOCATION:Lecture room A\, Watson building
CONTACT:Alexandra Tzella
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