|DATE||December 10 (Thu), 2020|
|INSTITUTE||University of South Florida|
|TITLE||Asymptotic analysis 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 present the major ideas in the asymptotic analysis of the Riemann-Hilbert problem that we constructed in the last lecture.?We also argue how the result may be useful to study the above mentioned limiting process.