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SUMMARY:Anton Kapustin (Caltech)
DTSTART:20240724T160000Z
DTEND:20240724T170000Z
DTSTAMP:20260423T005823Z
UID:TQFT/119
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TQFT/119/">T
 opological invariants of gapped states and cosheaves on sites</a>\nby Anto
 n Kapustin (Caltech) as part of Topological Quantum Field Theory Club (IST
 \, Lisbon)\n\n\nAbstract\nRecently\, an approach to constructing topologic
 al invariants of gapped ground-states of lattice systems has been develope
 d in our joint work with N. Sopenko. It applies to arbitrary gapped states
  of infinite-volume lattice spin systems with rapidly decaying interaction
 s and employs C*-algebraic techniques. In this talk\, I will explain an in
 terpretation of these invariants as obstructions to gauging\, i.e. to prom
 oting a symmetry to a local symmetry. The key observation is that locality
  on a lattice is an asymptotic notion sensitive only to the large-scale ge
 ometry of the support set. Following Kashiwara and Schapira\, one can enco
 de locality using a natural Grothendieck topology on a category of semilin
 ear subsets of Eucludean space. Infinitesimal symmetries of a gapped state
  form a cosheaf over the corresponding site\, and the topological invarian
 ts are encoded in its Cech complex.\n
LOCATION:https://researchseminars.org/talk/TQFT/119/
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