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SUMMARY:Dimitris Koukoulopoulos (Montreal)
DTSTART:20200608T160000Z
DTEND:20200608T170000Z
DTSTAMP:20260423T035636Z
UID:WAC/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WAC/4/">Galo
 is groups of polynomials of large degree</a>\nby Dimitris Koukoulopoulos (
 Montreal) as part of Webinar in Additive Combinatorics\n\n\nAbstract\nAbst
 ract: Let $\\mathcal{N}$ be a set of natural numbers and let us consider a
 ll monic polynomials of degree $n$ whose coefficients are in $\\mathcal{N}
 $. What are the odds that a polynomial chosen uniformly at random from thi
 s set is irreducible? Moreover\, what can we say about the distribution of
  its Galois group? I will present some recent results\, joint with Lior Ba
 ry-Soroker and Gady Kozma\, that show that if $\\mathcal{N}$ is not too sp
 arse\, then such random polynomials are highly likely to be irreducible an
 d have very large Galois group. The proofs uses a fun mixture of ideas fro
 m sieve methods\, the arithmetic of polynomials over finite fields\, prime
 s with restricted digits\, Galois theory and group theory.\n
LOCATION:https://researchseminars.org/talk/WAC/4/
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