070 Arno Kuijlaars

Arno Kuijlaars (Katholieke Universiteit Leuven, Belgium) // S-curves and critical measures on a Riemann surface // Abstract: Martinez-Finkelshtein and Rakhmanov introduced the notion of critical measure in the complex plane in order to characterize the limiting normalized zero counting measures of sequences of polynomials. Their main result is that critical measures are supported on contours with a symmetry property, so-called S-curves. We extend these notions to a compact Riemann surface. Our motivation to do this comes from random tiling models with periodic weights, which will also be discussed in the talk. This is joint work with Marco Bertola and Alan Groot