Integration of algebraic functions, polynomial approximation, nonclassical boundary problems and Poncelet-type theorems

Abstract: In this review talk we expose remarkably tight relations between the four topics mentioned in the title. Starting from the paper by N. H. Abel published in 1826 and subsequent results of Chebyshev and Zolotarev we finish at the recent results by Burskii, Zhedanov, Malyshev (et al.) devoted to algorithmic decidability of some identities for the values of the Weierstrass P-function, unexpected elementary geometric applications and many, many more hidden equivalences in seemingly unrelated areas of analysis, modern computer algebra and geometry. This talk will be given in Russian, the English version was presented on 16-09-2021 at Beijing-Novosibirsk seminar on geometry and mathematical physics ( english.math.pku.edu.cn/conferences/244.html ). The video and slides of that talk can be found at cloud.mail.ru/public/S4Pp/wJ5iFcggM

Russianmathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

( slides | video )

Mathematical models and integration methods