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SUMMARY:Carlos Florentino (Faculty of Sciences - University of Lisbon)
DTSTART:20211109T163000Z
DTEND:20211109T173000Z
DTSTAMP:20260423T022721Z
UID:Geolis/66
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Geolis/66/">
 The geometry of commuting varieties of reductive groups</a>\nby Carlos Flo
 rentino (Faculty of Sciences - University of Lisbon) as part of Geometria 
 em Lisboa (IST)\n\n\nAbstract\nLet $R_r(G)$ be the (connected component of
  the identity of the) variety of commuting $r$-tuples of elements of a com
 plex reductive group $G$. We determine the mixed Hodge structure on the co
 homology of the representation variety $R_r(G)$ and of the character varie
 ty $R_r(G)/G$\, for general $r$ and $G$. We also obtain explicit formulae 
 (both closed and recursive) for the mixed Hodge polynomials\, Poincaré po
 lynomials and Euler characteristics of these representation and character 
 varieties. In the character variety case\, this gives the counting polynom
 ial over finite fields\, and some results also apply to character varietie
 s of nilpotent groups.\n\nThis is joint work with S. Lawton and J. Silva (
 arXiv:2110.07060).\n
LOCATION:https://researchseminars.org/talk/Geolis/66/
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