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SUMMARY:The Story of Hodge Theory - Alexander Shannon (DPMMS)
DTSTART:20091012T150000Z
DTEND:20091012T160000Z
UID:TALK20842@talks.cam.ac.uk
CONTACT:Alexander Shannon
DESCRIPTION:This talk will start with an explanation of the celebrated the
 orem that the cohomology of a smooth projective complex algebraic variety 
 breaks up in a canonical way - the so-called Hodge decomposition. I shall 
 then go on to mention some of the ways this phenomenon generalises\, inclu
 ding Deligne's notion of a mixed Hodge structure\, which is carried by the
  cohomology of any complex algebraic variety and Griffiths' notion of a va
 riation of Hodge structure\, describing how the Hodge decomposition varies
  in families. Time-permitting\, I shall also explain some ways in which Ho
 dge structures appear in the more general setting of non-commutative algeb
 raic geometry\, and the efforts currently being made to study them.
LOCATION:MR5\, Centre for Mathematical Sciences
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