Fixed Points and Fair Divisions

What do the following two facts have in common?

(a) If you crumple up a map of Berkeley (without tearing) and place it on top of an identical map, there are two places in Berkeley whose images on the two maps lie one on top of the other.

(b) Three or more people (whose preferences are not too erratic) can always divide a cake amongst themselves so that each person thinks her piece is the largest piece.

Answer: they have almost exactly the same proof! Come to the talk to find out what that proof is. I'll also talk about a real-world application: how four Berkeley students sharing an apartment with unequal-size bedrooms can divide up their rent so that each person thinks he's getting the best of the deal.