Symmetric Solutions to Dispersionless 2D Toda Hierarchy, Hurwitz Numbers, and Conformal Dynamics

Sergey Natanzon, Anton Zabrodin

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

Abstract

We explicitly construct the series expansion for a certain class of solutions to the 2D Toda hierarchy in the zero dispersion limit, which we call symmetric solutions. We express the Taylor coefficients through some universal combinatorial constants and find recurrence relations for them. These results are used to obtain new formulas for the genus 0 double Hurwitz numbers. They can also serve as a starting point for a constructive approach to the Riemann mapping problem and the inverse potential problem in 2D.

Original languageEnglish
Pages (from-to)2082-2110
Number of pages29
JournalInternational Mathematics Research Notices
Volume2015
Issue number8
DOIs
Publication statusPublished - 2015
Externally publishedYes

Fingerprint

Dive into the research topics of 'Symmetric Solutions to Dispersionless 2D Toda Hierarchy, Hurwitz Numbers, and Conformal Dynamics'. Together they form a unique fingerprint.

Cite this