Frank Calegari

Aspects of the Eigencurve

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Abstract: I shall discuss some recent conjectures of Kevin Buzzard concerning classical modular forms and the Gouv\^ea--Mazur conjecture. Using some very naive techniques, Kevin and I have proved a special case of these conjectures. I shall try and describe the flavour of these calculations, as well as discussing other questions that arise from Buzzard's conjectures.