Isomonodromy and the accessory parameter problem for conformal maps

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• Bruno Carneiro da Cunha (Universidade Federal de Pernambuco)
• Friday 28 July 2023, 14:30-15:00
• Seminar Room 1, Newton Institute.

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CATW04 - Complex analysis: techniques, applications and computations - perspectives in 2023

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. This work was done in collaboration with Tiago Anselmo, Salman Abarghouei Nejad, Rhodri Nelson and Darren Crowdy

This talk is part of the Isaac Newton Institute Seminar Series series.

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