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DTSTART;TZID=America/New_York:20260923T150000
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DTSTAMP:20260917T190841Z
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UID:10013656-1790175600-1790179200@umaine.edu
SUMMARY:Prof. Eknath Ghate: Zig-zag holds for Galois representations
DESCRIPTION:Math Colloquium: September 23\, 2016\n3:00-4:05pm in Hill Auditorium\, Barrows Hall\nRefreshments at 3pm\, Talk at 3:15pm \nSpeaker: Prof. Eknath Ghate\nTitle: Zig-zag holds for Galois representations \nAbstract: Describing the shape of the reduction of local Galois representations attached to cusp forms\, at primes away from the level — or more generally\, the reduction of two-dimensional crystalline representations — remains an open problem. A folklore conjecture attributed to Breuil\, Buzzard and Emerton predicts that the reduction is irreducible if the weight is even and the slope is fractional. \nIn this talk we state and prove the zig-zag conjecture\, which treats the case of large exceptional weights and half-integral slopes. The conjecture predicts that the reduction alternates between certain irreducible and reducible representations\, in a pattern governed by the relative size of two auxiliary parameters. Special cases of zig-zag have previously been established using Langlands correspondences.
URL:/calendar/event/prof-eknath-ghate-zig-zag-holds-for-galois-representations/
LOCATION:Hill Auditorium\, Barrows Hall\, University of Maine\, Orono\, ME\, 04469\, United States
CATEGORIES:Lectures & Seminars
GEO:44.8922637;-68.6714486
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