On roots of random polynomials
 

The study of roots of random polynomials is an active area of research that has been ongoing since the early 1900s. In this talk, I will survey several recent developments, with an emphasis on robust frameworks that enable proofs of universality across a wide class of models. Topics will include global and local correlation structures of zeros, concentration phenomena, persistence probabilities, variance asymptotics for the number of real roots and CLT fluctuations.