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SUMMARY:Dualizability and orientability of tensor categories - David Jorda
 n (University of Edinburgh)
DTSTART:20170123T143000Z
DTEND:20170123T153000Z
UID:TALK70139@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:A topological field theory is an invariant of oriented&nbsp\;m
 anifolds\, valued in some category C\, with many pleasant properties. &nbs
 p\;According to the cobordism hypothesis\, a fully extended --&nbsp\;a.k.a
 . fully local --&nbsp\;TFT is uniquely determined by a single object of C\
 , which we may think of as&nbsp\;the invariant assigned by the theory&nbsp
 \;to the point. &nbsp\;This object must have strong finiteness properties\
 , called dualizability\, and strong symmetry properties\, called orientabi
 lity.<br><br>In this talk I&#39\;d like to give an expository discussion o
 f several recent works "in dimension 1\,2\, and&nbsp\;3"&nbsp\;-- of Schom
 mer-Pries\,&nbsp\;Douglas--Schommer-Pries--Snyder\, Brandenburg-Chivrasitu
 -Johnson-Freyd\, Calaque-Scheimbauer&nbsp\;-- which unwind the abstract no
 tions of dualizability and orientability into notions very familiar to the
  assembled audience: &nbsp\;things like Frobenius algebras\, fusion catego
 ries\, pivotal fusion categories\, modular tensor categories. &nbsp\;Final
 ly in this context\, I&#39\;ll discuss some work in progress with Adrien B
 rochier and Noah Snyder\, which finds a home on these shelves for arbitrar
 y tensor and&nbsp\;pivotal tensor&nbsp\;categories (no longer finite\, or 
 semi-simple)\, and for braided and ribbon braided tensor categories.<br>
LOCATION:Seminar Room 1\, Newton Institute
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