Date: Tuesday, April 26, 2016
Location: Rockefeller Hall 310
Title: Big finite numbers and big infinite numbers
Abstract: The following game is fun to play with a friend: each of you secretly writes down a number on a sheet of paper. Whoever's number is larger wins that round. Keep playing rounds until one of you is consistently winning every round. Then that person wins!
I will give a strategy for winning this game, which will involve considering certain algebraic systems which do not satisfy associativity. Unfortunately, in order for my strategy to work, I need to assume that certain big infinite numbers called large cardinals exist. This seems like a strange situation, but I will try to convince you that this fact suggests not only that these large cardinals do exist, but that they're actually interesting objects to study.