An introduction to the exact WKB analysis via the hypergeometric differential equation
- Date
- February 19 (Mon) at 9:00 - February 22 (Thu) at 17:00, 2024 (JST)
- Speaker
-
- Takashi Aoki (Professor Emeritus, Faculty of Science and Engineering, Kinki University)
- Venue
- Seminar Room #359 (Main Venue)
- via Zoom
- Language
- English
- Host
- Ryo Namba
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
[Contents]
- Introduction
- Exact WKB analysis for ordinary differential equation of second order with a large parameter
- Some classical theory for the Airy equation and the Gauss hypergeometric equation
- Exact WKB analysis for the Airy equation
- Exact WKB analysis for the Gauss hypergeometric equation
- Some applications and recent topics
This is a closed event for scientists. Non-scientists are not allowed to attend. If you are not a member or related person and would like to attend, please contact us using the inquiry form. Please note that the event organizer or speaker must authorize your request to attend.