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SUMMARY:Joachim Jelisiejew (University of Warsaw)
DTSTART:20200519T150000Z
DTEND:20200519T160000Z
DTSTAMP:20260423T041113Z
UID:NASO/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NASO/22/">Ad
 ditive group actions\, formal solutions to PDEs and Bialynicki-Birula deco
 mposition</a>\nby Joachim Jelisiejew (University of Warsaw) as part of Max
  Planck Institute nonlinear algebra seminar online\n\n\nAbstract\nLet $X$ 
 be a smooth projective variety over $\\mathbb{C}$ with an action of $(\\ma
 thbb{C}\, +)$. Assume that $X$ has a unique fixed point $x_0$. Carrell’s
  conjecture predicts that $X$ is rational. Restriction of orbits to germs 
 at $x_0$ reduces this conjecture to describing solutions of certain system
 s of PDE in the formal power series ring $k[[t]]$ with $d(t) = -t^2$. This
  suggests a stronger form of the conjecture: $X$ is a union of affine spac
 es. This strengthening would give an analogue of Bialynicki-Birula decompo
 sition for $(\\mathbb{C}\, +)$.\nIn the talk I will explain the beautiful 
 basics on how the $(\\mathbb{C}\, +)$-actions\, differential equations and
  rationality intertwine and then present the state of the art on the conje
 cture. This is a work in progress\, comments and suggestions are welcome!\
 n
LOCATION:https://researchseminars.org/talk/NASO/22/
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