BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dimitris Koukoulopoulos (Montreal) DTSTART:20200608T160000Z DTEND:20200608T170000Z DTSTAMP:20260404T143402Z UID:WAC/4 DESCRIPTION:Title: Galois groups of polynomials of large degree\nby Dimitris Koukoulop oulos (Montreal) as part of Webinar in Additive Combinatorics\n\n\nAbstrac t\nAbstract: Let $\\mathcal{N}$ be a set of natural numbers and let us con sider all monic polynomials of degree $n$ whose coefficients are in $\\mat hcal{N}$. What are the odds that a polynomial chosen uniformly at random f rom this set is irreducible? Moreover\, what can we say about the distribu tion of its Galois group? I will present some recent results\, joint with Lior Bary-Soroker and Gady Kozma\, that show that if $\\mathcal{N}$ is not too sparse\, then such random polynomials are highly likely to be irreduc ible and have very large Galois group. The proofs uses a fun mixture of id eas from sieve methods\, the arithmetic of polynomials over finite fields\ , primes with restricted digits\, Galois theory and group theory.\n LOCATION:https://stable.researchseminars.org/talk/WAC/4/ END:VEVENT END:VCALENDAR