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SUMMARY:Is a typical polynomial irreducible? Very Likely! - Dr Oleksiy Klu
 rman\, University of Bristol
DTSTART:20260320T180000Z
DTEND:20260320T190000Z
UID:TALK245875@talks.cam.ac.uk
CONTACT:133159
DESCRIPTION:What does a “typical” polynomial look like? Suppose we bui
 ld a polynomial of degree n by choosing each coefficient independently and
  at random to be either (+1) or (-1). A natural question then arises: *how
  likely is such a polynomial to be irreducible over the integers?*\n\nDesp
 ite how simple this question sounds\, it remains largely open and has attr
 acted a great deal of attention from mathematicians. Over the years\, rese
 archers have discovered that understanding random polynomials requires ide
 as from many different areas of mathematics.\n\n\n\nIn this talk\, we will
  take a journey through the mathematics behind this problem. We will start
  with classical results about polynomial irreducibility dating back to the
  19th century\, and then move toward modern perspectives on random polynom
 ials. Along the way\, we will see how tools from different fields come tog
 ether to tackle this deceptively simple question\, ending with some exciti
 ng developments that appeared as recently as last few years.\n\nNo prior b
 ackground in probability or advanced algebra will be assumed.
LOCATION:CMS\, MR2
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