The singularity probability of a random symmetric matrix

Combinatorics Seminar
Friday, November 4, 2022 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 202
Matthew Jenssen – University of Birmingham –
Anton Bernshteyn

Let $A$ be drawn uniformly at random from the set of all $n \times n$ 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.