In 2017, Miller computed the character tables of $S_n$ for all $n$ up to $38$ and looked at various statistical properties of the entries. Characters of symmetric groups take only integer values, and, based on his computations, Miller conjectured that almost all entries of the character table of $S_n$ are divisible by any fixed prime power as $n$ tends to infinity. Previously, Sound and I proved this conjecture for any fixed prime. In this talk, I will discuss joint work with Sound that fully resolves it, and mention some related open problems.

Note regarding location: The Pillsbury room is located on Floor 4M on the Psychology side of East Hall. To get to the room, you enter the Psychology side of East Hall from the Church Street entrance and before you get into the Psych atrium, there is an elevator to your left. Take the elevator to Floor 4M and the elevator opens into the room.