BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yuan Liu (Univ. of Michigan) DTSTART:20201201T210000Z DTEND:20201201T220000Z DTSTAMP:20260423T041500Z UID:UAANTS/9 DESCRIPTION:Title: P resentations of Galois groups of maximal extensions with restricted ramifi cations\nby Yuan Liu (Univ. of Michigan) as part of University of Ariz ona Algebra and Number Theory Seminar\n\n\nAbstract\nIn this talk\, we are going to discuss how to use Galois cohomology to study the presentation o f Galois groups of maximal extensions with restricted ramifications. In pr evious work with Melanie Matchett Wood and David Zureick-Brown\, we conjec ture that an explicitly-defined random profinite group model can predict t he distribution of the Galois groups of maximal unramified extension of gl obal fields that range over $\\Gamma$-extensions of $\\mathbb{Q}$ or $\\ma thbb{F}_q(t)$. In the function field case\, our conjecture is supported by the moment computation\, but very little is known in the number field cas e. Interestingly\, our conjecture suggests that the random group should si mulate the maximal unramified Galois groups\, and hence suggests some part icular requirements on the structure of these Galois groups. In this talk\ , we will prove that the maximal unramified Galois groups are always achie vable by our random group model\, which verifies those interesting require ments.\n LOCATION:https://researchseminars.org/talk/UAANTS/9/ END:VEVENT END:VCALENDAR