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BEGIN:VEVENT
DTSTAMP:20200210T114343Z
DTSTART:20200206T143000Z
DTEND:20200206T153000Z
SUMMARY:Ted Voronov: Supergeometry and the (Frobenius-Kolmogorov-Gelfand-
) Buchstaber-Rees theory
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}cfm-k68q4p5
8-3tto8o
DESCRIPTION:Title: Supergeometry and the (Frobenius-Kolmogorov-Gelfand-)B
uchstaber-Rees theory\n\nAbstract:\n\nVictor Buchstaber and Elmer Rees\,
motivated by the study of n-valued groups\, introduced a generalization
of ring homomorphisms under the name of "Frobenius n-homomorphisms". (B
ecause of the connection with Frobenius's work on "higher characters".)
Their central geometric result is an extension of the Gelfand-Kolmogorov
theorem---describing a topological space in terms of its algebra of con
tinuous functions---to symmetric powers of a topological space. It turns
out that ideas from supergeometry can help to simplify and generalize t
he theory of Buchstaber and Rees. (I do not mean by that a "superanalog"
.) The ideas come from our study of Berezinians and super exterior power
s. Very roughly\, while the Buchstaber-Rees theory tells what a sum of r
ing homomorphisms is (as everybody knows\, it is not a homomorphism)\, o
ur theory tells what the difference or actually an arbitrary integral li
near combination of ring homomorphisms are.\n\nThe talk is based on join
t works with H. Khudaverdian. We were brought to recall these works rece
ntly because of passing away of Elmer Rees in October 2019 (to whose mem
ory the talk is dedicated).
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams Room 1\, Alan Turing Building\, Manchester
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