BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jeff Manning (Imperial College London) DTSTART:20221123T160000Z DTEND:20221123T170000Z DTSTAMP:20260418T064041Z UID:LNTS/79 DESCRIPTION:Title: Th e Wiles-Lenstra-Diamond numerical criterion over imaginary quadratic field s\nby Jeff Manning (Imperial College London) as part of London number theory seminar\n\nLecture held in Huxley 139\, Imperial.\n\nAbstract\nWile s' modularity lifting theorem was the central argument in his proof of mod ularity of (semistable) elliptic curves over Q\, and hence of Fermat's Las t Theorem. His proof relied on two key components: his "patching" argument (developed in collaboration with Taylor) and his numerical isomorphism cr iterion.\n\nIn the time since Wiles' proof\, the patching argument has bee n generalized extensively to prove a wide variety of modularity lifting re sults. In particular Calegari and Geraghty have found a way to generalize it to prove potential modularity of elliptic curves over imaginary quadrat ic fields (contingent on some standard conjectures). The numerical criteri on on the other hand has proved far more difficult to generalize\, althoug h in situations where it can be used it can prove stronger results than wh at can be proven purely via patching.\n\nIn this talk I will present joint work with Srikanth Iyengar and Chandrashekhar Khare which proves a genera lization of the numerical criterion to the context considered by Calegari and Geraghty (and contingent on the same conjectures). This allows us to p rove integral "R=T" theorems at non-minimal levels over imaginary quadrati c fields\, which are inaccessible by Calegari and Geraghty's method. The r esults provide new evidence in favor of a torsion analog of the classical Langlands correspondence.\n LOCATION:https://researchseminars.org/talk/LNTS/79/ END:VEVENT END:VCALENDAR