Курс лекций профессора В.Паскье Институт Теоретической Физики, Гиф-сюр-Иветт, Франция

"Topics from the theory of integrable systems" (based on joint works with O.Babelon, J.Shiraishi and Y.Tutiya)

1) Solution of Toda, Toda-Ruisjenaars  (Calogero-Sutherland-Ruisjenaars) models  by Bethe ansatz).
2) Hirota tau functions for Benjamin-Ono equation from quantum models,  connection with Baxter Q matrix and Macdonald polynomial Pieri rules.
3) Solution of non-conservative open chain in connection with ASEP.
4) Connections between the preceding lectures 1) and 2)  and Hall  Effect with Seiberg Witten AGT, shuffle and Schiffmann Vasserot algebras.