The Stokes Phenomenon and Some Applications

TL;DR

This paper reviews multisummation and its role in describing Stokes matrices, explores moduli spaces related to Stokes phenomena, and demonstrates applications to Painlevé equations, quantum differential equations, and hypergeometric equations.

Contribution

It provides a comprehensive review of multisummation, computes explicit moduli spaces for Stokes matrices, and applies these concepts to various differential equations.

Findings

Explicit moduli space for a third Painlevé equation

Demonstration of the monodromy identity's usefulness in quantum and hypergeometric equations

Clarification of the role of multisummation in describing Stokes phenomena

Abstract

Multisummation provides a transparent description of Stokes matrices which is reviewed here together with some applications. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for a third Painlev\'e equation is made explicit. It is shown that the monodromy identity, relating the topological monodromy and Stokes matrices, is useful for some quantum differential equations and for confluent generalized hypergeometric equations.