The theory of elliptic curves is one of the most active but also one of the most mysterious in modern number theory. At its most basic level, it originates from one of the oldest problems in mathematics, that of finding integer solutions to various polynomial equations, and yet, despite this, it lies at the heart of many current advances of which Andrew Wiles' recent proof of Fermat's Last Theorem is a notable example. Their definition is a deceptively simple one: an elliptic curve can generally be defined as the set of solutions to certain cubic equations of the form . Things start to get interesting when we define a very elementary operation on this set which turns it into a group: the resulting structure is one of the deepest and richest in mathematics. So, join us this Monday at 7:30 in MS.05 as we take a look at the fascinating world of elliptic curves and continue with our theme of explaining the most important currently unsolved problems as we touch on the Birch and Swinnerton Dyer Conjecture, another of the seven Millenium Prize Problems. We then head off to the pub for drinks and banter.