The singularity probability of a random symmetric matrix

Let A be drawn uniformly at random from the set of all n x n symmetric matrices with entries in {-1,1}. What is the probability that A is singular? This is a classical problem at the intersection of probability and combinatorics. I will give an introduction to this type of question and sketch a proof that the singularity probability of A is exponentially small in n. This is joint work with Marcelo Campos, Marcus Michelen and Julian Sahasrabudhe.