北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

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关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
行政团队
学术研究
研究团队
公开课
讨论班
招生招聘
教研人员
博士后
学生
会议
学术会议
工作坊
论坛
学院生活
住宿
交通
配套设施
周边旅游
新闻
新闻动态
通知公告
资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > Hypergeometric Functions
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.
讲师
沈大立
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.
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.
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.
北京雁栖湖应用数学研究院
CONTACT

No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

北京市怀柔区 河防口村544号
北京雁栖湖应用数学研究院 101408

Tel. 010-60661855
Email. administration@bimsa.cn

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