The first talk of 2012 in the Quantitative Finance Seminar series was given this week by Bruno Dupire.
As I mentioned when I was introducing his talk, the Dupire equation is not the best known result in mathematical finance - that honour has to go to the Black-Scholes equation. But the Black-Scholes equation is an oversimplification of reality that most people try to stay away from as much as possible, whereas the Dupire equation, in the words of Alex Lipton who spoke at Fields in November, is the "most effective result in mathematical finance."
Bruno spoke about yet another remarkable innovation that he has produced in recent years, what he calls Functional Ito Calculus, and its uses in the context of path dependent options. I think it's a fascinating result and have asked him to expand his paper into a short book format to be published as one of the first volumes of the soon to be launched Springer Briefs in Quantitative Finance.