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SUMMARY:Lior Bary-Soroker (Tel Aviv University)
DTSTART:20201014T150000Z
DTEND:20201014T160000Z
DTSTAMP:20260423T040008Z
UID:hnts/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/9/">Ran
 dom polynomials\, probabilistic Galois theory\, and finite field arithmeti
 c</a>\nby Lior Bary-Soroker (Tel Aviv University) as part of Heilbronn num
 ber theory seminar\n\n\nAbstract\nIn the talk we will discuss recent advan
 ces on the following two questions:\nLet $A(X) = \\sum ±X^i$ be a random 
 polynomial of degree n with coefficients taking the values $-1\, 1$ indepe
 ndently each with probability $1/2$.\n\nQ1: What is the probability that $
 A$ is irreducible as the degree goes to infinity?\n\nQ2: What is the typic
 al Galois group of $A$?\n\nOne believes that the answers are YES and THE F
 ULL SYMMETRIC GROUP\, respectively.\nThese questions were studied extensiv
 ely in recent years\, and we will survey the tools developed to attack the
 se problems and partial results.\n
LOCATION:https://researchseminars.org/talk/hnts/9/
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