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SUMMARY:Magnitude homology - Tom Leinster (University of Edinburgh)
DTSTART:20170530T131500Z
DTEND:20170530T141500Z
UID:TALK71947@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:Magnitude homology is a homology theory of enriched categories
 \, proposed by Michael Shulman late last year.  For ordinary categories\, 
 it is the usual homology of a category (or equivalently\, of its classifyi
 ng space).  But for metric spaces\, regarded as enriched categories à la 
 Lawvere\, magnitude homology is something new.  It gives truly metric info
 rmation: for instance\, the first homology of a subset X of R^n detects wh
 ether X is convex.\n\nLike all homology theories\, magnitude homology has 
 an Euler characteristic\, defined as the alternating sum of the ranks of t
 he homology groups.  Often this sum diverges\, so we have to use some form
 al trickery to evaluate it. In this way\, we end up with an Euler characte
 ristic that is often not an integer.  This number is called the "magnitude
 " of the enriched category. In topological settings it is the ordinary Eul
 er characteristic\, and in metric settings it is closely related to volume
 \, surface area and other classical invariants of geometry.
LOCATION:MR5\, Centre for Mathematical Sciences
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