|DATE||December 08 (Tue), 2020|
|INSTITUTE||University of South Florida|
|TITLE||Planar orthogonal polynomials and the construction of the Riemann-Hilbert problem|
|ABSTRACT||In the Coulomb gas model the Coulomb particles may condense to form a droplet in the thermodynamic limit. Cusp singularities in the droplet have been classified by Sakai and the local process near the cusp has been studied by Wiegmann and company using physical argument.?More recently a rigorous study of cusp singularities by Ameur, Kang, Makarov and Wennman could show the existence of a limiting process near cusps.
We will overview the relation between the orthogonal polynomials?and the Coulomb gas system. Using the conformal map constructed in the previous lecture, we will construct the Riemann-Hilbert problem that is satisfied by the orthogonal polynomial. This is a joint?work with Meng Yang.