Bruno Carneiro da Cunha - Isomonodromy and the accessory parameter problem for conformal maps

Описание к видео Bruno Carneiro da Cunha - Isomonodromy and the accessory parameter problem for conformal maps

Abstract: A classical result in complex analysis relates the uniformizing map of a given simple domain to the ratio of solutions of a second order ordinary differential equation of the Fuchsian type. Despite its simplicity, the usefulness of this relation to the actual construction of the map has been hindered by the problem of fixing the parameters of the equation given the geometrical information of the domain. In this talk we will outline a solution for this problem for simply-connected domains bounded by arcs of circles, as well as present the new type of special functions involved in the solution, the semi-classical conformal block. We will illustrate the technique by considering a few examples numerically.

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