Claude Sabbah - On coalescing singularities in isomonodromic deformations

Abstract: A result of Cotti, Dubrovin and Guzzetti asserts (roughly) that in an isomonodromic deformation of an irregular differential equation of Poincaré rank one and regular semi-simple polar coefficient, the deformation extends to non regular semi-simple polar coefficients only if some specific entries of the Stokes matrix vanish. An analytic approach by Fourier transformation has been given by Guzzetti. We propose a topological explanation of this result by means of the notion of intermediate extension of a local system and topological formulas for the Stokes matrix after Fourier-Laplace transform.