An introduction to the exact WKB analysis via the hypergeometric differential equation

This is an introductory course to the exact WKB analysis. Firstly we review some basic facts concerning formal power series and WKB solutions. Secondly we give an overview of the connection formulas for WKB solutions to ordinary differential equations of second order with a large parameter. Next, after recalling some classical theory for the Airy equation and the Gauss hypergeometric differential equation, we show how the exact WKB analysis is used for these equations and what are obtained. One of the main results to be presented in this course is the relation the between the classical hypergeometric function and the Borel resummed WKB solutions to the hypergeometric differential equation with a large parameter. Some applications and recent topics are also given.

[Schedule (Tentative)]
Day 1
10:00 - 11:30 Lecture 1
14:00 - 16:00 Lecture 2

Day 2
10:00 - 11:30 Lecture 3
14:00 - 16:00 Lecture 4

Day 3
10:00 - 11:30 Lecture 5
14:00 - 16:00 Lecture 6

Day 4
10:00 - 11:30 Lecture 7
14:00 - 16:00 Lecture 8