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SUMMARY:The Galois group of random reciprocal polynomials [MPIM]
DTSTART:20250527T123000Z
DTEND:20250527T133000Z
DTSTAMP:20260420T161200Z
UID:indico-event-436@math-events.uni-bonn.de
DESCRIPTION:Speakers: David Hokken (Utrecht University)\n\nNumber theory l
 unch seminar\nLet $P = a_m T^m + \\sum_{j=0}^{m-1} a_j (T^{m-j} + T^{m+j})
 $ be a monic reciprocal polynomial of even degree n\, with the a_j drawn i
 ndependently and uniformly at random from {1\, 2\, …\, H} for some fixed
  integer H ≥ 35. In joint work with Dimitris Koukoulopoulos\, we show th
 at P is irreducible over the rationals\, and has large Galois group\, with
  probability tending to 1 as n tends to infinity. This agrees\, in a setti
 ng of coefficients with ‘mild’ dependencies\, with the long-helf belie
 f going back in various forms to Hilbert\, Van der Waerden\, Odlyzko―Poo
 nen and Konyagin that a typical polynomial is irreducible and has Galois g
 roup as large as possible. I will discuss some aspects of the proof\, whic
 h draws from classical polynomial theory\, Fourier analysis\, probability 
 theory and group theory\, and explain why the dependence of the coefficien
 ts of P does (not) matter. \n\nhttps://math-events.uni-bonn.de/event/436/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/436/
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