El Seminario Iberoamericano de Matemáticas - SIM 116 se celebra el día 29 de junio de 2022 en las Casas del Tratado de Tordesillas, con el siguiente programa:
13:00-14:00 Moulay Barkatou (U. Limoges):
On Solvability of Linear differential systems with small coefficients.
We are interested in the problem of solvability, in the Liouvillian sense (or, by generalized quadratures), of linear differential systems with small coefficients . For a general system, this problem is equivalent to that of solvability of the Lie algebra of the differential Galois group of the system. However, the dependence of his Lie algebra on the system coefficients remains unclear. We show that for the particular class of systems with non-resonant irregular singular points that have sufficiently small coefficient matrices, the problem is reduced to that of checking the solvability of the explicit Lie algebra generated by the coefficient matrix of the system. This generalizes the corresponding Ilyashenko--Khovanskii for linear differential systems with Fuchsian singular points. We will present a few examples illustrating the practical verification of our criteria of solvability by using general procedures implemented in Maple.
This talk is based on a joint work with Renat Gontsov (from IITP of RAS).
16:30-17:30 Mark Spivakovsky (CNRS Institut de Mathématiques de Toulouse):
μ-Constant families of Newton non-degenerate singularities admit simultaneous embedded desingularization.
We will begin this talk with a brief summary of different notions of equisingularity in families of isolated hypersurface singularities, concentrating on various notions of simultaneous desingularization.
We will then report on joint work with Max Leyton and Hussein Mourtada. The starting point of this work is a 1980 paper by Yujiro Kawamata in which the author claims to relate the existence of simultaneous embedded resolution in a family to the property of the family being μ*-constant. Inspired by this paper, we formulated two conjectures relating the notions of μ-constant, μ*-constant and simultaneous embedded resolution. We will discuss our proof of the first of the two conjectures and illustrate it with the example of Briançon – Speder.