На 11 септември 2025 г. от 17:00 часа в Заседателната зала на ФМИ ще се проведе поредната сбирка на колоквиума на ФМИ.
Доклад ще изнесе професор Ги Казал (Guy Casale) от Университет Рен, Франция.
Тема на доклада:
Irreducibility of the Painlevé Equations through Differential Galois Theory
Резюме на доклада:
A differential equation of order n is said to be reducible if one can obtain its general solution by solving lower order differential equations and linear differential equation (see Stockholm lessons by Painlevé in 1895). The question the irreducibility of the Painlevé equations was solved by the Japanese School around 1988-1997. At the same time, H. Umemura and independently B. Malgrange developed a Galois theory for non-linear differential equation and hoped to apply it to the irreducibility problem.
I will present some properties of the Malgrange pseudogroup implying the irredudibility of the differential equation.
The computation of Malgrange pseudogroup is very difficult in general, but when we know an algebraic solution, we can compute the Galois group of the linear variational equations and compare it to the Malgrange pseudogroup.
This program has been applied to (many) Painlevé equations by Casale+Weil and latter Acosta+Casale+Weil. I will present the technique used and the difficulties in the remaining cases.
Преди лекцията, от 16:30 часа участниците в колоквиума са поканени в Заседателната зала на неформална дискусия на кафе/чай.