It's near Portofino, famous for its big yachts full of rich tourists, but I didn't get that far. The food was great, though, and it was nice to see the lazy waves of the Mediterranean, so different from the oceans I know and love. I spoke about n-categories, with only the barest mention of their possible relevance to computer science. What's neat is that I almost understood some of these talks, thanks to the fact that category theory provides a highly general language for talking about processes. As we simulate more and more physics with better and better computers based on more and more physics, it seems almost inevitable that physics and computer science will come to be seen as two ends of a more general theory of processes.
Computer scientists like to define functions recursively.
Similarly, physicists like to define functions by differential equations. A fixed-point theorem is something that says there exists a solution, preferably unique, of this sort of equation. The principle of mathematical induction says that any operator F of this sort has a unique fixed point. You might wonder how Picard's theorem is proved. I'll sketch this idea, leaving out all the details.