Type: Seminar

Distribution: World

Expiry: 11 Sep 2012

Auth: gilesg@bari.maths.usyd.edu.au

Speaker: Jonanthan Zhu (MIT) Abstract: A key paradigm in modern number theory is the parametrisation of elliptic curves by modular forms. In particular, Wiles’ proof of Fermat’s last theorem relies on one such correspondence, which has now been generalised to a much larger class of elliptic curves. After introducing the basic concepts and examples of modular forms, I will do my best to one-up Max by stating the major steps in the proof of Fermat’s last theorem. Modular forms also arise in somewhat unexpected ways, for example in the Witten genus and in the theory of monstrous moonshine, which is concerned with the Monster group. If time permits, I will discuss these observations and some generalisations of the theory of modular forms.