# Nic Fellini (Queen's University)

Date

Monday January 23, 20234:30 pm - 5:30 pm

Location

Jeffery Hall, Room 319## Number Theory Seminar

**Monday, January 23rd, 2023**

**Time:** 4:30 p.m. **Place:** Jeffery Hall, Room 319

**Speaker:** Nic Fellini (Queen's University)

**Title:** The bipartite sieve and applications to probabilistic Galois theory

**Abstract:** Given a monic polynomial f of degree n in Z[x], one can ask: what is the probability that the Galois group of f is a proper subgroup of the symmetric group on n symbols? This probabilistic Galois theory question has been studied for nearly 90 years! The most "satisfying" answer to this question is due to P. Gallagher in 1973. The key part of Gallagher's proof is the use of the multidimensional large sieve. The goal of this talk is to develop a much simpler sieve--- the bipartite sieve ---to study the probabilistic Galois theory question. Time permitting, we will discuss other applications of the bipartite sieve.