GAINS · Geometric Aspects of Integrable Nonlinear Systems

The issues of the research project are focused on the theory of integrable systems and its relation to the field theories. The first objective is further development of the theory of the integrability preserving dispersive deformations of integrable dispersionless systems. Next is the formulation of the classical R-matrix approach to the Frobenius manifolds. Another objective is the revision of the theory of Whitham hierarchies related to the moduli spaces of Riemann surfaces of all genera. The last research objective is to begin the programme on quantization of Whitham hierarchies of all genera, i.e. construction of dispersionful Whitham hierarchies. In our research we are going in general to apply methods of differential algebraic geometry. If the Marie Curie Intra-European Fellowship will be awarded, the proposed research will take place in the research group Integrable Systems and Mathematical Physics at the Department of Mathematics of the University of Glasgow. Scientists from the host institution are leading scientists in the subjects considered in this project. The scientist in charge of the supervision of the project is Dr. Ian Strachan. Training in the above broad perspectives will give me possibility of improving of my knowledge of the theory of integrable systems and its relations with other branches of mathematical physics like Frobenius manifolds. The experience gained will bring me closer to become a fully professional and independent scientist. All these together will contribute to completion and diversification of my expertise.