Type: Seminar

Distribution: World

Expiry: 29 Aug 2012

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

Speaker: Max Menzies (Cambridge) COMPLEX ELLIPTIC CURVES You might have heard of elliptic curves before, from other mathematicians or even the media. There are two reasons for their fame: first, they were important in the proof of Fermat’s Last Theorem, the most famous mathematical problem in the world; secondly, they are awesome. Perhaps the prettiest family of objects in all of maths. I will not prove Fermat’s Last Theorem, because it is... hard. Yeah, it’s quite difficult. But I will introduce elliptic curves and discuss their nicest properties. In general, it’s quite hard to define and understand elliptic curves, because they are objects of projective geometry, rather than plane geometry. However over the complex numbers, they have a surprising and beautiful geometric equivalence with something you all know and love (to eat). This is the simplest example of an deep relationship between algebraic geometry (objects defined by polynomial equations) and analytic geometry (complex manifolds).