The theme of the lecture course “Advanced Study of Nonlinear Mechanics” held during the week 24-28 June 2019 was “Poisson geometry, moduli spaces, and applications”. Poisson geometry is a generalization of symplectic geometry, and both play a fundamental role in the modern theory of mechanics. Although Poisson geometry is named after the distinguished French mathematician Simeon Denis Poisson (1781-1840), its systematic development began only in the 1980’s.
The principal lecturers were Prof. Yvette Kosmann-Schwarzbach (formerly of the Ecole Polytechnique, France) and Prof. Nan-Kuo Ho (National Tsing-Hua University, Taiwan). Prof. Yvette Kosmann-Schwarzbach is one of the creators of modern Poisson geometry, and her lecture course “Introduction to Poisson geometry” was an impressive survey of the theory, from its early history to its current status. Prof. Nan-Kuo Ho’s course “Applications of Poisson geometry and related topics” focused on applications to moduli spaces of flat connections, an area to which she has made major contributions. Several additional “guest lectures” were given by other specialists, who described further applications, illustrating the wide scope of this field.
The lectures attracted a large audience of students and researchers from Waseda and from other universities. Poisson himself was both an educator and a researcher, and he is reputed to have said “Life is good for only two things, doing mathematics and teaching it”. This Super Global course truly exemplified Poisson’s philosophy!