Dr Alan Thompson - Mirror Symmetry: the great mathematical story you've (probably) never heard...

In this talk I'll tell one of the great stories of modern mathematics: the discovery of the phenomenon called "mirror symmetry" in algebraic geometry. We'll start at the end of the 19th Century, with Hilbert's 23 unsolved problems that would go on to define much of 20th Century mathematics. Of interest to us is the 15th problem, which laid the foundations for the modern theory of enumerative geometry. An important problem in enumerative geometry was Clemens' Conjecture but, despite years of work by numerous mathematicians, in 1990 this conjecture was still considered completely intractable.

Meanwhile, in the 1980's, theoretical physics was abuzz with excitement about the new ideas of string theory. But the physicists had their own problems: they could not find a way to get consistent answers out of string theory, due to ambiguities in the way the theory was set up. This led them to the idea of "mirror symmetry": a proposed relationship between two different formulations of string theory. Unbeknownst to them, this new idea was about to turn the world of enumerative geometry on its head...

In this talk I will tell this fascinating story and, if there's enough time left at the end, I'll speak a little bit about how the story is still being written and what part I'm hoping to play in that endeavour.