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CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20231013T092157Z
DTSTART:20231204T133000Z
DTEND:20231204T143000Z
SUMMARY:Manchester Geometry Seminar - Andrey Lazarev
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}v23z-lnoegl
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DESCRIPTION:Speaker: Professor Andrey Lazarev (Lancaster)\n\nTitle: Homot
opy gauge equivalence of Maurer-Cartan elements\n\nAbstract: A Maurer-Ca
rtan (MC) element in a differential graded algebra (dga) A is an element
x satisfying the equation of flat connection dx+x^2=0. Two MC elements
x and y are gauge equivalent if there is an invertible element a in A su
ch that x=aya^{-1}-daa^{-1}. The set of MC elements in A modulo gauge eq
uivalence is called the MC moduli set of A. These are well-known and cla
ssical notions familiar to experts in differential geometry and deformat
ion theory. It is also well-known that the moduli set of MC elements is
not a quasi-isomorphism invariant of a dga. In this talk I will explain
how one can usefully weaken the notion of a gauge equivalence so that it
leads to the MC moduli set becoming a homotopy invariant (in a certain
precise sense). This is the beginning of a long story\, with many intere
sting ramifications of which I will attempt to outline a few. Nontrivial
examples come from de Rham and Dolbeault algebras.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams Room\, Alan Turing Building\, Manchester
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