Hypergeometric Functions
The classical hypergeometric function was introduced by Euler in the 18th century, and was extensively studied in the 19th century by Gauss, Riemann, Schwarz and Klein, among others. For its frequent occurrences in many branches of science, it was then generalized naturally in two directions: with more parameters and in more variables. It turns out that these functions pack a lot of information: geometric, algebraic, arithmetic and so on. To name a few, they, as a guiding example, lead to the formulation of the Riemann–Hilbert Problem (#21 in Hilbert’s famous list of problems), and they even have a connection with the Prime Number Theorem.
In this course, I will give a basic introduction to the properties of various hypergeometric functions, with an emphasis on the monodromy of their accompanying hypergeometric equations.
In this course, I will give a basic introduction to the properties of various hypergeometric functions, with an emphasis on the monodromy of their accompanying hypergeometric equations.
讲师
日期
2023年09月18日 至 12月13日
位置
Weekday | Time | Venue | Online | ID | Password |
---|---|---|---|---|---|
周一,周三 | 09:50 - 11:25 | A3-4-101 | ZOOM 07 | 559 700 6085 | BIMSA |
修课要求
Complex analysis
课程大纲
(1) Linear differential equations and monodromy.
(2) The Euler–Gauss hypergeometric functions.
(3) The Clausen–Thomae hypergeometric functions.
(4) The Lauricella hypergeometric functions.
(5) Throughout the course I will mention and discuss some related open problems, which would arise naturally in the course of the discussion.
(2) The Euler–Gauss hypergeometric functions.
(3) The Clausen–Thomae hypergeometric functions.
(4) The Lauricella hypergeometric functions.
(5) Throughout the course I will mention and discuss some related open problems, which would arise naturally in the course of the discussion.
参考资料
[1] F. Beukers, Gauss’ hypergeometric function, 2009, available at https://webspace.science.uu.nl/~beuke106/GaussHF.pdf
[2] F. Beukers, Hypergeometric functions in one variable, 2008, available at https://webspace.science.uu.nl/~beuke106/springschool99.pdf
[3] G. Heckman, Tsinghua lectures on hypergeometric functions, 2015, available at https://www.math.ru.nl/~heckman/tsinghua.pdf
[4] E. Looijenga, Uniformization by Lauricella functions – an overview of the theory of Deligne-Mostow, in: Arithmetic and geometry around hypergeometric functions, Progress in Mathematics 260, Birkhäuser Verlag Basel, 2007, 207–244.
[2] F. Beukers, Hypergeometric functions in one variable, 2008, available at https://webspace.science.uu.nl/~beuke106/springschool99.pdf
[3] G. Heckman, Tsinghua lectures on hypergeometric functions, 2015, available at https://www.math.ru.nl/~heckman/tsinghua.pdf
[4] E. Looijenga, Uniformization by Lauricella functions – an overview of the theory of Deligne-Mostow, in: Arithmetic and geometry around hypergeometric functions, Progress in Mathematics 260, Birkhäuser Verlag Basel, 2007, 207–244.
视频公开
公开
笔记公开
公开
语言
英文
讲师介绍
Dali Shen is an assistant professor at BIMSA currently. His research is focused on algebraic geometry and complex geometry. He obtained his PhD from Utrecht University. Before joining BIMSA, he held postdoc positions at IMPA and TIFR.