Speaker: Krishan Canzius

Abstract: Imagine you and your friends are trying to decide where to go for dinner. You all have your own personal ranking of the options but somehow you need to combine your individual rankings into a group ranking. If you were hoping that math could help you with this problem then you’re out of luck! It turns out that there is no fair way to solve this type of problem, and ultrafilters are to blame! In this talk we’ll sketch a proof of Arrow’s Impossibility Theorem using ultrafilters. Then we’ll see how ultrafilters can be used to construct non-standard models of the reals and natural numbers: structures which look a lot like the ones we are familiar with despite containing infinitesimals and infinitely large numbers.