Dr Frazer Jarvis

Dr Jarvis works in the area of algebraic number theory, an area which uses techniques from algebra, algebraic geometry and classical number theory, amongst others. In particular, he studies the relationship between modular forms, elliptic curves and representations of Galois groups. That this is currently an active area of research is clear from the recent proof of Fermat's Last Theorem by Andrew Wiles; Wiles uses exactly these methods in his proof. Dr Jarvis is particularly interested in generalisations of these ideas (known as the Langlands Philosophy), and even in possible generalisations of Fermat's Last Theorem. For example, one might ask whether the Fermat equation of a given degree (or a similar equation) has solutions in a given field extension of the rationals. Within this speciality, there are a number of possible research topics.