Global Study of Differential Equations in the Complex Domain

Global Study of Differential Equations in the Complex Domain. Polish-Japanese research group

1 September, 2013 -  7 September, 2013 | Warsaw



The main objective of the project is to continue and develop the study of linear and nonlinear ordinary and partial differential equations in the complex domain by a variety of methods: formal solutions, asymptotic analysis, WKB methods, Borel and moment summability, middle convolution, methods of the theory of integrable systems and special functions. We also put special emphasis on the global study like monodromy and connection problems of linear and nonlinear ordinary differential equations on the basis of the above mentioned collaborations. The main goal is to strengthen existing and start new collaborations between Polish and Japanese leading researchers working in these fields.

We plan to organize 2 morning plenary lectures from Monday to Friday and 2 afternoon plenary lectures or (less formal) seminars, where works in progress or open problems may be discussed.

Main topics:
Formal solutions of non-kovalevskian equations (Borel summability of the heat equation on manifolds, characterization of Borel summable solutions of linear PDEs with variable coefficients, application of moment summability to study of formal solutions of PDEs)
Special functions (application of the WKB method to hypergeometric equations related with some generating functions for the Multiple Zeta Values, the study of special functions via middle convolution, the hierarchies of the Painlevé equations)



The conference is co-financed by:

Warsaw Center of Mathematics and Computer Science