## Number Theory - Steven Spallone (IISER Pune)

### Wednesday, May 22nd, 2019

**Time:** 3:30-4:30 p.m. **Place:** Jeffery Hall 319

**Speaker:** Steven Spallone (IISER Pune)

**Title:** Divisibility of Character Values of Symmetric Groups

**Abstract:** Fix a permutation $\sigma$ in some symmetric group $S_k$, and consider it as sitting in $S_n$ for $n \geq k$. Also fix a positive integer $d$. The probability that an irreducible character $\chi$ of $S_n$ evaluated at $\sigma$ will be a multiple of $d$ approaches $100\%$ as $n$ approaches infinity. We will sketch a proof, which is joint work with Jyotirmoy Ganguly and Amritanshu Prasad.