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SUMMARY:Entropy is inevitable  - Tom Leinster\, Edinburgh
DTSTART:20130219T141500Z
DTEND:20130219T151500Z
UID:TALK42451@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:The title refers not to the death of the universe\, but to the
  fact that the concept of entropy is present in the pure-mathematical hear
 tlands of algebra and topology\, whether we like it or not.  I will descri
 be a categorical machine which\, when fed as input the concepts of topolog
 ical simplex and real number\, produces as output the concept of Shannon e
 ntropy.  The most important component of this machine is the notion of "in
 ternal algebra" in an algebra for an operad (generalizing the notion of mo
 noid in a monoidal category).  There is more: the resulting characterizati
 on of Shannon entropy can be stripped completely of its categorical garb\,
  giving a simple\, new\, and entirely elementary characterization.  This l
 ast theorem is joint with John Baez and Tobias Fritz.\n
LOCATION:MR5\, Centre for Mathematical Sciences
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