SUMS: Zhu -- Modular forms - How to prove Fermat in four easy steps

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.