论文标题
关于数学问题的Riemann-Hilbert问题的起源
On the origins of Riemann-Hilbert problems in mathematics
论文作者
论文摘要
首先，本文是对Riemann-Hilbert问题理论的历史性回顾，特别是在希尔伯特（Hilbert）的第21个问题和Plemelj与之相关的工作的背景下，其最初的出现。本说明的次要目的是邀请新一代的数学家进入Riemann-Hilbert Techniques的迷人世界及其在非线性数学物理学中的现代外观。我们着手以六个示例来实现这一目标，包括Amir，Corwin，Quastel \ cite {acq}的全面差异性painlevé-ii公式的新证明，该公式在KPZ交叉分布的描述中输入。本文的一部分基于作者的全体演讲，在奥地利Hagenberg的正交多项式，特殊功能和应用程序（OPSFA）上举行了15美元的国际研讨会。
This article is firstly a historic review of the theory of Riemann-Hilbert problems with particular emphasis placed on their original appearance in the context of Hilbert's 21st problem and Plemelj's work associated with it. The secondary purpose of this note is to invite a new generation of mathematicians to the fascinating world of Riemann-Hilbert techniques and their modern appearances in nonlinear mathematical physics. We set out to achieve this goal with six examples, including a new proof of the integro-differential Painlevé-II formula of Amir, Corwin, Quastel \cite{ACQ} that enters in the description of the KPZ crossover distribution. Parts of this text are based on the author's plenary lecture at the $15$th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA) in Hagenberg, Austria.
