Seminar series
Date
Mon, 01 Nov 2010
Time
15:45 -
16:45
Location
L3
Speaker
Tom Leinster
Organisation
Glasgow
There is a close but underexploited analogy between the Euler characteristic
of a topological space and the cardinality of a set. I will give a quite
general definition of the "magnitude" of a mathematical structure, framed
categorically. From this single definition can be derived many
cardinality-like invariants (some old, some new): the Euler characteristic
of a manifold or orbifold, the Euler characteristic of a category, the
magnitude of a metric space, the Euler characteristic of a Koszul algebra,
and others. A conjecture states that this purely categorical definition
also produces the classical invariants of integral geometry: volume, surface
area, perimeter, .... No specialist knowledge will be assumed.