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SUMMARY:À la recherche de l'âme tordue
DTSTART:20230517T120000Z
DTEND:20230517T130000Z
DTSTAMP:20260522T144600Z
UID:indico-event-9886@indico.math.cnrs.fr
DESCRIPTION:Speakers: Rafal Suszek (Warsaw)\n\nThe fundamental role of hig
 her geometry – that of (n-)gerbes realising integral classes in the de R
 ham cohomology of manifolds and of the attendant higher categories – in 
 the description of dynamics of (extended) distributions of charge and Maxw
 ell-type gauge fields – such as σ-models and certain topological field 
 theories – has\, by now\, been well established. Higher geometry (HG) de
 termines a (pre-)quantisation of the dynamics\, captures its rigid and gau
 ge symmetries as well as dualities (such as\, e.g.\, T-duality)\, models d
 efects etc. In the talk\, a generalisation shall be presented of Murray's
  formulation of HG to the Berezin-Leïtes-Kostant Z/2Z-graded geometry wit
 h Lie-supergroup `symmetries' – a natural setting of the so-called super
 -σ-models of Green and Schwarz. The generalisation\, taking as its point 
 of departure the supersymmetric refinement of the de Rham cohomology\, cal
 ls for a conceptual reworking of the differential-geometric tools employed
  in the un-graded setting – a replacement\, i.a.\, of the usual Čech an
 d Beilinson-Deligne techniques by purely algebraic ones based on the Kosta
 nt-Leïtes approach to Lie supergroups and the cohomology of their Lie sup
 eralgebras. And yet\, by the end of the day\, the ensuing HG objects – t
 he super-n-gerbes – are seen to encode/resolve\, just as their Murray's 
 predecessors\, a nontrivial `topology' – that of the Soul of certain non
 -Rothstein superorbifolds of their bases. Thus\, they provide an intricate
  reinterpretation of the aforementioned supersymmetric refinement of the d
 e Rham cohomology\, consistent with Freed's functorial definition of the u
 nderlying superfield theories. This shall be demonstrated with the help of
  a suitable adaptation of the equivariantisation techniques and of the gau
 ge-defect construction for the two-dimensional σ-model worked out\, once 
 upon a temps perdu\, in a joint venture with Gawędzki\, Runkel and Waldor
 f. \n\nhttps://indico.math.cnrs.fr/event/9886/
LOCATION:Fokko du Cloux (Bâtiment Braconnier)
URL:https://indico.math.cnrs.fr/event/9886/
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