Solvability of linear differential systems with small exponents in the Liouvillian sense

The talk is devoted to the solvability of linear diff erential systems by quadratures, one of the classical problems of differential Galois theory. Solvability of a system depends entirely on properties of its differential Galois group. However, to detect the solvability or non-solvability of a given system is a difficult problem, as dependence of its differential Galois group on the coefficients of the system remains unknown. We consider systems with regular singular points as well as those with irregular ones whose exponents are sufficiently small. For systems satisfying such restrictions criteria of solvability can be given in terms of the coefficient matrix.