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SUMMARY:Irreducibility of random reciprocal polynomials
DTSTART:20261012T090000Z
DTEND:20261012T100000Z
DTSTAMP:20261013T105500Z
UID:indico-event-17013@indico.math.cnrs.fr
CONTACT:regis.de-la-breteche@imj-prg.fr
DESCRIPTION:Speakers: David Hokken (Max Planck Institute\, Allemagne)\n\nL
 et $P = a_m T^m + \\sum_{j=0}^{m} a_j (T^{m-j} + T^{m+j})$ be a monic reci
 procal polynomial of even degree n\, with the $a_j$ drawn independently an
 d uniformly at random from $\\{1\, 2\, \\ldots\, H\\}$ for some fixed inte
 ger $H \\geq 35$. In joint work with Dimitris Koukoulopoulos\, building on
  prior work of Bary-Soroker—Koukoulopoulos—Kozma\, we show that $P$ is
  irreducible over the rationals\, and has large Galois group\, with probab
 ility tending to 1 as $n$ tends to infinity. This is in line with the long
 -held belief going back in various forms to Hilbert\, Van der Waerden\, Od
 lyzko—Poonen and Konyagin that a typical polynomial is irreducible and h
 as Galois group as large as possible. I will discuss some recent\, related
  developments in the field of probabilistic Galois theory before discussin
 g aspects of the proof\, which draws from classical polynomial theory\, Fo
 urier analysis\, probability theory and group theory.\n\nhttps://indico.ma
 th.cnrs.fr/event/17013/
LOCATION:Salle Yvette Cauchois (IHP - Bâtiment Perrin)
URL:https://indico.math.cnrs.fr/event/17013/
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