BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:David Roberts (University of Minnesota\, Morris) DTSTART:20251014T203000Z DTEND:20251014T213000Z DTSTAMP:20260423T130519Z UID:MITNT/126 DESCRIPTION:Title: Wild Ramification in Hypergeometric Motives\nby David Roberts (Univers ity of Minnesota\, Morris) as part of MIT number theory seminar\n\nLecture held in Room 2-449 in the Simons Building (building 2).\n\nAbstract\nThe bulk of my talk will be an overview of the current state of knowledge of w ild ramification in general hypergeometric motives at a fixed prime $p$. The presentation will be as elementary and visual as possible\, using p-ad ic ordinals of field discriminants of trinomials $x^n - n t x + (n-1) t$ and their underlying Galois theory as a continuing example. It will be re vealed that the general situation is very complicated\, but exhibits enoug h patterns that one can still reasonably hope for a universal formula iden tifying all numerical invariants of wild p-adic ramification in all hyperg eometric motives.\n\nIf one restricts to the case where $\\operatorname{or d}_p(t)$ is coprime to $p$ then the situation simplifies considerably. Th e ramp conjecture of Section 13 of my survey on Hypergeometric Motives wit h Fernando Rodriguez Villegas predicts conductor exponents. I will concl ude with a new refinement of the ramp conjecture that predicts\, via Feynm an-like diagrams\, how the conductor exponents decompose as a sum of slope s. The refinement reveals much more structure than the original ramp con jecture\, and I hope will point the way to a proof.\n LOCATION:https://researchseminars.org/talk/MITNT/126/ END:VEVENT END:VCALENDAR