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. Nonscientists 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.