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
Location: MSRI: Simons Auditorium
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.
If none of the options work for you, you can always buy the DVD of this lecture. The videos are sold at cost for $20USD (shipping included). Please Click Here to send an email to MSRI to purchase the DVD.
See more of our Streaming videos on our main VMath Videos page.