Mathematics & Statistics research seminar
Pizza and soft drinks will be served after the talk.
SPEAKER: Dr. Yulia Bibilo
ABSTRACT: The Hilbert's 21st problem was formulated as follows: show that there always exists a linear di fferential equation of a Fuchsian type (or a Fuchsian system) with given poles and a given monodromy representation. The problem is closely connected to so called isomonodromic deformations and integrability of nonlinear differential equations. In general the Hilbert's 21st problem has negative solution. There have been a number of studies to obtain necessary and sufficient conditions for a required Fuchsian system to exist. In the talk, we present an approach to get explicit solutions of this problem via middle convolution.