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SUMMARY:Aaron Landesman (MIT)
DTSTART:20230210T200000Z
DTEND:20230210T210000Z
DTSTAMP:20260407T214913Z
UID:agstanford/108
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/agstanford/1
 08/">Splitting types of finite monodromy vector bundles</a>\nby Aaron Land
 esman (MIT) as part of Stanford algebraic geometry seminar\n\nLecture held
  in Room 383-N.\n\nAbstract\nGiven a finite degree $d$ cover of curves $f:
  X \\to \\mathbb P^1$\, we study $f_* \\mathscr O_X$\, which is a rank $d$
  vector bundle on $\\mathbb P^1$\, hence\ncan be written as a direct sum o
 f line bundles \n$f_* \\mathscr O_X \\simeq \\oplus_{i=1}^d \\mathscr O(a_
 i)$.\nNaively\, one might expect that if the cover above is general\, this
  vector bundle is balanced\, meaning that the $a_i$'s are as close to each
  other as possible.\nWhile this is not quite true\, we explain what can be
  said about these splitting types\, by studying how they change as we defo
 rm the cover. This is based on joint work with Daniel Litt.\n\nThe ideas c
 ropping up here were also instrumental in resolving\nconjectures of Esnaul
 t-Kerz and Budur-Wang regarding the density of geometric local\nsystems in
  the moduli space of local systems.\n
LOCATION:https://researchseminars.org/talk/agstanford/108/
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