Infinities Make for the Best Parties

In this talk, we'll introduce a few delightful topics about infinities (choice functions, countable and uncountable infinities, Ramsey theory, and the independence of the continuum hypothesis) by hosting a party with infinitely-many guests! We'll first play a game with hats (choice functions; also, who doesn't like a good hat?). Then we'll try to organize people into groups to encourage social mingling (Ramsey theory). We'll see that our ability to do this is affected not just by how large of an infinity of guests we have, but also by whether or not we are working in a world where the continuum hypothesis holds.