Author Description

The conference on which these proceedings are based was held at the Chinese University of Hong Kong. It was organized in response to Andrew Wiles' conjecture that every elliptic curve over Q is modular. The final difficulties in the proof of the conjectural upper bound for the order of the Selmer group attached to the symmetric square of a modular form, have since been overcome by Wiles with the assistance of R. Taylor. The proof that every semi-stable elliptic curve over Q is modular is not only significant in the study of elliptic curves, but also due to the earlier work of Frey, Ribet, and others, completes a proof of Fermat's last theorem.