Simon Myerson, Undergraduate Mathematics Seminar
This is the second of two seminars on this topic, but it is completely independent and no prior knowledge is required.
In 1659 Pierre de Fermat claimed to have “astonished the greatest experts” with his methods of ascent and descent. They were the first attempt at a systematic approach to solving polynomial equations in whole numbers (Diophantine equations). Descents – in a form which would have greatly astonished Fermat – are used today in research on the ‘hot topic’ of elliptic curves. In this seminar we will introduce some concepts from algebraic geometry (divisors, meromorphic functions on curves, descent), and see how closely related these are to Fermat’s ideas.