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BEGIN:VEVENT
DTSTAMP:20210209T105413Z
DTSTART:20210216T130000Z
DTEND:20210216T140000Z
SUMMARY:Manchester Algebra Seminar - Matt Booth
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DESCRIPTION:Speaker: Matt Booth \n\n\nTitle: Mac Lane cohomology and to
pological Hochschild cohomology\n\n\nAbstract: The deformation theory of
an algebra over a field is controlled by its Hochschild cohomology\, an
d in particular square-zero extensions of A are bijection with HH^2(A).
For general rings\, Hochschild cohomology does not capture enough inform
ation\, and one must use a cohomology theory called Mac Lane cohomology
instead\, which records nonlinear data.\n\nI'll begin the talk by descri
bing the above picture\, and then report on ongoing joint work with Dmit
ry Kaledin and Wendy Lowen where we try to generalise this situation to
abelian categories\, which one can view as many-object rings. We start b
y showing that for rings\, Mac Lane cohomology agrees with topological H
ochschild cohomology\, an invariant constructed using techniques from al
gebraic topology - the analogous statement for homology has been known s
ince the 90s. This allows us to define the Mac Lane cohomology of an abe
lian category.\n\n\nIn particular\, we get a definition for the Mac Lane
cohomology of an algebraic variety\, and using some powerful invariance
techniques for THH we're able to do some quite explicit computations.\n
\n\n\nTime: 1pm\nPlace: Zoom
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Zoom - online\, Alan Turing Building\, Manchester
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