The pseudospectrum of polynomials in random matrices

The pseudospectrum of an operator is the set of "almost eigenvalues" in the complex plane. Pseudospectra are important for quantifying the stability of numerical algorithms involving non-normal matrices. In recent years there has been enormous progress on understanding the pseudospectrum of random matrices with iid entries. In this talk I will discuss some extensions to quadratic polynomials in iid matrices. Based on joint work with Alice Guionnet and Jonathan Husson.