Oradora: Galina Filipuk, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland

Título: On the Heun equation

Data, hora e local: 9 de julho de 2021, às 14h, na plataforma Zoom no seguinte endereço

https://videoconf-colibri.zoom.us/j/85998937178?pwd=ZUdIWm5IRFNEb0dTZDF6Z2x5U3l4Zz09

Resumo/Abstract: Heun equation is a Fuchsian equation with 4 singuarities. It appears in many areas of mathematical physics. It has a lot of nice properties. Moreover, in particular cases it can be reduced to the hypergeometric equation. It also has applications in the theory of orthogonal polynomials. In this talk I shall present some results on the Heun equation based on the following papers:

 — Filipuk, G.; Ishkhanyan, A.; Derezinski, J. On the derivatives of the Heun functions. Izv. Nats. Akad. Nauk Armenii Mat. 55 (2020), no. 3, 21–29.
— Chen, Y.; Filipuk, G.; Zhan, L. Orthogonal polynomials, asymptotics, and Heun equations. J. Math. Phys. 60 (2019), no. 11, 113501, 34 pp.
— Vidunas, R.; Filipuk, G. A classification of coverings yielding Heun-to-hypergeometric reductions. Osaka J. Math. 51 (2014), no. 4, 867–903.
— Vidunas, R.; Filipuk, G. Parametric transformations between the Heun and Gauss hypergeometric functions. Funkcial. Ekvac. 56 (2013), no. 2, 271–321.
— Filipuk, G. V. A hypergeometric system of the Heun equation and middle convolution. J.
Phys. A 42 (2009), no. 17, 175208, 11 pp.

Funded by the Portuguese Government through the FCT – Fundação para a Ciência e a Tecnologia under the project UIDB/00212/2020.