101 Andrei Martinez-Finkelshtein

Andrei Martinez-Finkelshtein (Baylor University, USA and University of Almería, Spain) // On the flow of zeros of derivatives of polynomials // Abstract Assume we have a sequence of polynomials whose asymptotic zero distribution is known. What can be said about the zeros of their derivatives? Especially if we differentiate each polynomial several times, proportional to their degree? This simple-to-formulate problem has recently attracted the attention of several researchers. Both the problem and the methods of its solution have exciting connections with free probability, random matrices, and approximation theory on the complex plane. This is a partial survey in which I will explain some known results in this direction and our approach to the problem. This is a joint work in progress with E. Rakhmanov from the University of South Florida.