Charles Alley : The Stokes phenomenon and Monodromy of the Airy Equation: A Case Study

Posted by David Reynolds , part of the Graduate Analysis Seminar.

At

April 4, 2018, 4 p.m.

In

SEO 512

Abstract

Several powerful theorems allow us to describe the asymptotics of solutions to ordinary differential equations in the complex domain. The Stokes phenomenon refers to the multivalued behavior of formal solutions of equations with irregular singularities or, put another way, that there are "jumps" in the asymptotics of the solutions. The associated Stokes data, which I will define, can be thought of as an enriching of the monodromy data of differential equations. Understanding this has led to a rich geometric program. In this talk, and a talk to follow, I will describe the analytic foundations of this program while focusing on the example of the Airy equation $u'' + zu=0$, which has an irregular singularity at infinity.