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SUMMARY:Open-closed bordisms and TFTs - Adela Zhang (Københavns Universit
 et (University of Copenhagen))
DTSTART:20250618T104500Z
DTEND:20250618T114500Z
UID:TALK230698@talks.cam.ac.uk
DESCRIPTION:An E_1 Calabi-Yau object A in a symmetric monoidal infinity-ca
 tegory C is a dualizable E_1 algebra together with an S^1-cyclic trace tha
 t exhibits a self duality of A. Examples include the cochain complex of an
 y closed oriented manifold. By work of Barkan and Steinebrunner\, every E_
 1 Calabi-Yau object in C defines a 2-dimensionsional "open" field theory w
 ith values in C\, which are symmetric monoidal functors from the open 2-bo
 rdism category O to C. In upcoming work with Barkan and Steinebrunner\, we
  show that any open field theory F extends canonically to an open-closed f
 ield theory whose value at the circle is the THH of the E_1 Calabi-Yau obj
 ect A associated to F. As a corollary\, we obtain an action of the moduli 
 spaces of surfaces on the THH of E_1 Calabi-Yau algebras. This provides a 
 space level refinement of previous work of Costello (over Q) and Wahl (ove
 r Z).
LOCATION:Seminar Room 1\, Newton Institute
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