Timur Sadykov: Universal bases in analytic solutions spaces to differential equations and monodromy calculation

In my talk, I will present a recent joint work with Susumu Tanabe. A small deformation of a holonomic system of partial differential equations can drastically change the branching properties of its holomorphic solutions. Besides, generically good bases in the space of local analytic solutions to such a system can exhibit complicated behaviour as the parameters of the system approach their singular values. I will discuss this phenomenon and present a way to construct universal bases (that is, bases whose elements remain lineraly independent under any perturbation of the system in question) for a class of holonomic bivariate systems of partial differential equations. As a corollary, a method to compute monodromy representations for such systems will be presented.