Anastasia Frolova - Limit zero distributions of Heine-Stieltjes polynomials

Title: Limit zero distributions of Heine-Stieltjes polynomials.

Abstract: The seminar is based on the paper "Critical measures, Quadratic Differentials, and Weak Limits of Zeros of Stieltjes polynomials" by A. Martínez-Finkelshtein, E. A. Rakhmanov. We consider Heine-Stieltjes polynomials - polynomial solutions of Lamé equation. We define extremal and critical measures in order to study limit zero distributions of such polynomials. We investigate connections of quadratic differentials with critical measures.