Professor Alexander Its and Professor Elizabeth Its (Indiana University Purdue University Indianaoplis, USA) gave a mini-course at Waseda University 20-22 November 2017. The course was an introduction to the Riemann Hilbert method and its applications. This is a mathematical technique which has its origins in the 19th Century theory of special functions (Bessel functions, Airy functions, etc) which has been very fundamental in mathematics and physics for more than 100 years.
The 19th Century theory treats functions which are solutions of linear differential equations. It is a much more difficult task to treat functions which are solutions of nonlinear differential equations (for example Painleve equations) – and the Riemann Hilbert method does this. These equations also have many applications in physics, such as matrix models, combinatorics, and statistical mechanics. The systematic development of the Riemann Hilbert method started around the 1980’s, and it is now a very active field of research.
Professor Alexander Its is a distinguished researcher in this area, and a major contributor to the development of the theory, and he has received many honours and accolades for his work. He began the mini-course with a survey of the theory starting from the basics of complex function theory. This was much appreciated by the audience consisting of students and researchers with different backgrounds. Then several applications were explained by him and by Professor Elizabeth Its. The mini-course was a very educational introduction to top-level mathematics and its scientific
applications.
・The abstract of the mini-course
・Unit for “Multiscale Analysis, Modeling and Simulation”
