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SUMMARY:Hodge polynomials of the moduli space of SL (2\,C) - character var
 ieties - Logares\, M (ICMAT)
DTSTART:20110203T153000Z
DTEND:20110203T163000Z
UID:TALK29649@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Let X be a compact Riemann surface  of genus g. SL(2\,C)-chara
 cter varieties of X are rich objects which lie in the intersection of alge
 braic geometry\, complex geometry\, and differential geometry. While they 
 are diffeomorphic to moduli spaces of Higgs bundles\, as algebraic varieti
 es they are very different. Character varieties are affine\, while Higgs m
 oduli spaces are foliated by the fibers of the Hitchin map which are compa
 ct algebraic subvarieties. There has been much work investigating the mixe
 d Hodge structures on the cohomology groups of these character varieties\,
  and their Hodge polynomials have been computed using number theoretical t
 echniques.\n\nOur goal is to compute the Hodge polynomial of SL(2\,C)-char
 acter varieties\, by stratifying these spaces in such a way that Hodge str
 ucture theory gives simpler formulas for the strata\, so we are allowed to
  compute the whole polynomials in terms of the Hodge polynomials of the st
 rata. This is work in progress with V. Muoz and P. Newstead.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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