Юни
17
2026
От draganova
Уважаеми колеги,
На 25 юни 2026 г. от 16:00 часа в Заседателната зала на ФМИ ще се проведе поредната сбирка на Колоквиума на ФМИ, на която ще бъдат изнесени два доклада от френски математици.
- От 16:00 часа е докладът на проф. Guy Casale (University of Rennes)
Следват заглавието и резюме на доклада му:
Ax-Schanuel theorem for order 1 algebraic differential equation (a work in progress with Rémi Jaoui and Gabriel Barbosa)
Abstract :
Ax Schanuel type theorems are statement describing the algebraic relations between solutions of a differential equation evaluated in some formal power series. The main example is
Thm(Ax) : If x_1, ..., x_n are non constant formal power series and
transc.deg. C(x_1, .... x_n, exp(x_1), ...exp(x_n)) / C < 1+n then
there exists a non trivial linear relation c_1x_1 + ... + c_n x_n =d
with c_j in Z and d in C.
I will present a generalisation of this theorem to non transversally projective, codimension one, holomorphic (singular) foliation. The main consequence will be
Thm : Let dy/dx = P(x,y)/Q(x,y) be a generic algebraic differential
equation with P,Q polynomial of degree d > 1 and f be a solution at 0.
If x_1, ..., x_n are non constant formal power series vanishing at 0 and
transc.deg. C(x_1, .... x_n, f(x_1), ...f(x_n)) / C < 1+n then there
exist i < j such that x_i = x_j. - Вторият доклад е от 17:30 часа и ще бъде изнесен от проф. Jacques-Arthur Weil (University of Limoges)
Следват заглавието и резюмето на доклада му:
Malgrange pseudogroups of Painlevé equations
Abstract:
The Malgrange groupoid is one of the generalizations of the Galois group to nonlinear differential equations. Introduced about twenty years ago, its theory has been well developed. However, its computation generally remains beyond our reach. In this project, a collaboration with Guy Casale and Primitivo Acosta-Humanez, we use a major result of Casale, generalizing the work of Morales and Ramis: when a differential equation is linearized along an algebraic solution, the Galois groups of the linearized equations can be viewed as sub-objects of the Malgrange group. This has allowed our group to establish an effective criterion for the dimension of these differential Galois groups to determine the Malgrange groupoids of Painlevé equations that admit an algebraic solution. The presentation will be supported by examples that will demonstrate the entire process and show most of the calculations performed partly manually and partly with computers.
В паузата между двата доклада (17:00 - 17:30 часа) участниците в колоквиума ще могат да проведат неформални дискусии на кафе/чай и сладки.