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SUMMARY:Vesselin Dimitrov (University of Toronto)
DTSTART:20200930T150000Z
DTEND:20200930T160000Z
DTSTAMP:20260423T040114Z
UID:hnts/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/3/">No 
 shadowing bounds on Galois orbits in the complex plane</a>\nby Vesselin Di
 mitrov (University of Toronto) as part of Heilbronn number theory seminar\
 n\n\nAbstract\nFor varying pairs of non-isogenous abelian varieties of a g
 iven dimension over a given finite field\, what is the least possible arcl
 engths sum under a matching of their Frobenius roots? For varying pairs of
  Salem numbers in $[1\,2]$\, what is their least possible distance in term
 s of the sum of their degrees?\n\nWe address\, and partly answer\, these k
 inds of questions in the seminar\, with a particular focus on the two repr
 esentatives at hand. The method\, which is based on potential theory in th
 e complex plane\, also establishes the Lehmer conjecture for the integer m
 onic polynomials $P(X)$ that have\nall their roots limited to the complex 
 disk $|z| < 10^{1/\\deg(P)}$: the extremal case where the Galois orbit of 
 algebraic integers is maximally equalized around the unit circle. We also 
 raise a few apparently new questions that our results motivate.\n
LOCATION:https://researchseminars.org/talk/hnts/3/
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