Dispersionless 2D Toda hierarchy, Hurwitz numbers and Riemann theorem

23rd International Conference on Integrable Systems and Quantum Symmetries

Mnatanzon, Sergey^1,2,3

National Research University Higher School of Economics, 20 Myasnitskaya street, Moscow

101000, Russia^1

Institute for Theoretical and Experimental Physics, 25 Bolshaya Cheremushkinskaya street, Moscow

117218, Russia^2

Laboratory of Quantum Topology, Chelyabinsk State University, 129 Brat'ev Kashirinykh street, Chelyabinsk

454001, Russia^3

关键词: Classical problems;    Connected domains;    Dispersionless;    Symmetric solution;    Toda hierarchy;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/670/1/012036/pdf
DOI  :  10.1088/1742-6596/670/1/012036

来源: IOP

【 摘 要 】

We describe all formal symmetric solutions of dispersionless 2D Toda hierarchy. This classification we use for solving of two classical problems: 1) The calculation of conformal mapping of an arbitrary simply connected domain to the standard disk; 2) Calculation of 2- Hurwitz numbers of genus 0.