I will give a brief overview of Wiles’ proof of Fermat’s Last Theorem, and explain the connection between modular forms and elliptic curves via Galois representations e.g. the Taniyama-Shimura conjecture. In the second half, I’ll explain some recent results on p-adic modular forms and deformations of Galois representations. If time permits, I’ll outline a future project on ranks of elliptic curves.

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- Seminars for 2008

Last updated: 24 Mar 2023