### The singularity probability of a random symmetric matrix

Combinatorics Seminar

7th February 2023, 11:00 am – 12:00 pm

Fry Building, 2.04

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.

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