Today's Noetherian Ring talk is cancelled.

The study of random polynomials has been investigated for many decades. In this talk, we will discuss several classical results together with recent developments and open problems in the field. We also discuss a general framework to prove universality results for correlation functions of the roots and apply it to study various questions on random polynomials, random trigonometric functions, and random eigenfunctions. Using these universality results, we study the mean and variance of the number of real roots. We also show that the number of real roots satisfies the Central Limit Theorem.

This talk is based on several joint papers with Mei-Chu Chang, Yen Do, Hoi Nguyen, and Van Vu.