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Analytic continuation of p-adic modular forms and applications to modularity

Introductory Workshop: New Geometric Methods in Number Theory and Automorphic Forms August 18, 2014 - August 22, 2014

August 18, 2014 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Payman Kassaei (McGill University)
Location: MSRI: Simons Auditorium
Video

Abstract

The lecture series will start with a  brief introduction to rigid analytic geometry. I will then introduce modular curves from various viewpoints (complex analytic, algebraic, and p-adic analytic) and use them to give a geometric definition of  p-adic and overconvergent modular forms and Hecke operators. I will next show how to use the p-adic geometry of the modular curves towards p-adic analytic continuation of overconvergent modular forms. Finally, I will demonstrate an application of these results to modularity of certain Galois representations which can itself be used to prove certain cases of the Artin conjecture. If time allows, I would explain briefly how these ideas extend to higher dimensions by illustrating the easier case of Hilbert modular surfaces.

Supplements
21408?type=thumb Kassaei Notes 469 KB application/pdf Download
Video/Audio Files

14049

H.264 Video 14049.mp4 335 MB video/mp4 rtsp://videos.msri.org/data/000/021/341/original/14049.mp4 Download
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