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SUMMARY:Payman Eskandari (University of Toronto)
DTSTART:20211028T185000Z
DTEND:20211028T195000Z
DTSTAMP:20260423T022925Z
UID:GPRTatNU/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GPRTatNU/39/
 ">The unipotent radical of the Mumford-Tate group of a very general mixed 
 Hodge structure with a fixed associated graded</a>\nby Payman Eskandari (U
 niversity of Toronto) as part of Geometry\, Physics\, and Representation T
 heory Seminar\n\n\nAbstract\nThe Mumford-Tate group $G(M)$ of a mixed Hodg
 e structure $M$ is a subgroup of $GL(M)$ which satisfies the following pro
 perty: any rational subspace of any tensor power of $M$ underlies a mixed 
 Hodge substructure if and only if it is invariant under the natural action
  of $G(M)$. Assuming $M$ is graded-polarizable\, the unipotent radical $U(
 M)$ of $G(M)$ is a subgroup of the unipotent radical $U_0(M)$ of the parab
 olic subgroup of $GL(M)$ associated to the weight filtration on $M$. Let u
 s say $U(M)$ is large if it is equal to $U_0(M)$.\n\nThis talk is a report
  on a recent joint work with Kumar Murty\, where we consider the set of al
 l mixed Hodge structures on a given rational vector space\, with a fixed w
 eight filtration and a fixed polarizable associated graded Hodge structure
 . It is easy to see that this set is in a canonical bijection with the set
  of complex points of an affine complex variety $S$. The main result is th
 at assuming some conditions on the (fixed) associated graded hold\, outsid
 e a union of countably many proper Zariski closed subsets of $S$ the unipo
 tent radical of the Mumford-Tate group is large.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/39/
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