Photos

Photos from Deirdre Haskell’s talk and dinner afterwards.

Title: An infinite pigeonhole principal

Abstract: The pigeonhole principle states that there is no injective function from a finite set to itself with one point removed. Equivalently, that any injective function from a finite set to itself is also surjective. This statement — every function on the set is injective if and only if surjective — can be taken to be the definition of a set being finite. On an infinite set, there are always functions that are injective but not surjective, so what can I possibly mean by an infinite pigeonhole principal?

In this talk, I will start by reminding you of the definitions of injective and surjective. Then we’ll look at examples of functions defined on some infinite sets in particular contexts, and see that, in many cases, these functions that illustrate the failure of the pigeonhole principal feel somehow unnatural. I’ll suggest a way in which we can capture what it might mean to be “unnatural”, and suggest a formulation of an infinite pigeonhole principal, with examples where it holds and where it fails.

WiMSoCal 2018 held at Pepperdine University

Photos from WiMSoCal 2017, held on February 11, 2017 at USC.