Automorphic types and Galois representations have performed a critical function within the improvement of contemporary quantity idea, with the previous coming to prominence through the distinguished Langlands application and Wiles' facts of Fermat's final Theorem. This two-volume assortment arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic kinds and Galois Representations' in July 2011, the purpose of which used to be to discover contemporary advancements during this sector. The expository articles and study papers around the volumes mirror fresh curiosity in p-adic tools in quantity conception and illustration idea, in addition to fresh development on issues from anabelian geometry to p-adic Hodge concept and the Langlands software. the themes lined in quantity one contain the Shafarevich Conjecture, powerful neighborhood Langlands correspondence, p-adic L-functions, the basic lemma, and different issues of up to date curiosity.
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