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SUMMARY:Sina Saleh (Harvard University)
DTSTART:20261109T210000Z
DTEND:20261109T220000Z
DTSTAMP:20261115T003412Z
UID:NTBU/59
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTBU/59/">Bi
 algebraic geometry of Böttcher coordinates</a>\nby Sina Saleh (Harvard Un
 iversity) as part of Boston University Number Theory Seminar\n\nLecture he
 ld in CDS Room 548 in Boston University.\n\nAbstract\nThe Böttcher coordi
 nate $\\Psi$ of a non-exceptional polynomial $f$ which is defined on a dis
 k $D$ centered at the origin and satisfies \n\n$\\Psi(z^d) = f(\\Psi(z))$\
 n\nwhere $d = deg(f)$\, is known to be transcendental. In this talk\, I wi
 ll discuss the associated $f$-bialgebraic sets\, that are\, algebraic bran
 ches in $D^n$ whose images under the coordinatewise map $(\\Psi \, ... \, 
 \\Psi)$ are again algebraic branches of the same dimension. Under mild ass
 umptions on the Julia set of $f$\, we obtain a complete classification of 
 these sets. I will also explain how this classification leads to an Ax–L
 indemann–Weierstrass type conjecture\, which we prove when the Julia set
  of $f$ is disconnected.\n\nNote this is NOT the usual room for this semes
 ter! This seminar is joint with the dynamics seminar\, and will be in CDS 
 548.\n
LOCATION:https://researchseminars.org/talk/NTBU/59/
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