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 M3//EN
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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20261005T102724Z
DTSTART:20261005T140000Z
DTEND:20261005T150000Z
SUMMARY:On super exterior powers and Berezinians 
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}m9u-muv3vld
 t-dcfd2b
DESCRIPTION:Abstract:\n\nI will speak about power expansions of the funct
 ion $R(z)=\\mathrm{Ber}(E+ zA)$\, where A is a linear operator in a supe
 rspace (or a supermatrix). Berezinian is the superanalog of determinant.
  Unlike the classical case\, is not a polynomial in the matrix entries b
 ut a rational function. Also\, it cannot be described in terms of the to
 p exterior power because no such top power exists in the super case. How
 ever\, a non-obvious connection between these notions exists\, and it is
  encoded in the properties of the expansions of $\\mathrm{Ber}(E+ zA)$. 
 (Due to Khudaverdian and myself\, also earlier work of Th. Schmitt.) For
  example\, "vanishing of top power" is replaced by "universal recurrent 
 relations" (satisfied by the supertraces or in the Grothendieck ring)\, 
 and $\\mathrm{Ber} A$ is expressed as the ratio of certain Hankel determ
 inants built of supertraces of exterior powers. There has been some inte
 resting new development (due to Ekanayaka-Shemyakova)\, which I can also
  speak about if time permits. 
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams room 1\, Alan Turing Building\, Manchester
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