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SUMMARY:Path integrals and state sums for general defect TQFTs - Kevin Wal
 ker (Microsoft (USA))
DTSTART:20250918T090000Z
DTEND:20250918T103000Z
UID:TALK235954@talks.cam.ac.uk
DESCRIPTION:For homogeneous\, defect-free TQFTs\, (1) n+\\epsilon-dimensio
 nal versions of the theories are relatively easy to construct\; (2) an n+\
 \epsilon-dimensional theory can be extended to n+1-dimensional (i.e. the t
 op-dimensional path integral can be defined) if certain more restrictive c
 onditions related to handle cancellation are satisfied\; and (3) applying 
 this path integral construction to a handle decomposition of an n+1-manifo
 ld yields a state sum description of the path integral. &nbsp\;In this tal
 k\, I'll show that the same pattern holds for defect TQFTs. &nbsp\;The ada
 ptation of homogeneous results to the defect setting is mostly straightfor
 ward\, with the only slight difficulty being the purely topological proble
 m of generalizing handle theory to manifolds with defects. &nbsp\;If time 
 allows\, I'll describe two applications: a Verlinde-like dimension formula
  for the dimension of the ground state of fracton systems\, and a generali
 zation\, to arbitrary dimension\, of Ostrik's theorem relating algebra obj
 ects to modules (gapped boundaries).
LOCATION:Seminar Room 2\, Newton Institute
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