Harmonic and Complex Analysis in the Problems of Mathematical Physics

General approaches of Harmonic Analysis provide a deep insight into a vast scope of modern topics of Real, Complex and Geometric Analysis and adjacent topics of Mathematical Physics and Mechanics. A wide variety of problems of Mathematical Physics and Flu id Mechanics can be intrinsically modeled in terms of geometric and analytic methods, in particular, being viewed under the Hamiltonian formalism. A deep interplay between Partial Differential Equations, Integrable Systems, Manifold Structures (Riemannian and non-Riemannian), Field Theory, Strings from one side, and Harmonic Analysis and Geometric Function Theory from the other one, allows us to concentrate our efforts in this project dedicated to creation new approaches and general methods of considering both these spectra of problems as well as to applications of these methods in Physics and Mechanics. The mainstream of the project is based on the following principle: any motion is geodesic with respect to certain action and certain metric. In particula r, the motion in the plane may be treated as a worldsheet of String Theory, and the description of such motion may be based on finding and studying correct actions, metrics, correlators, and finally, this will lead to construction of a complete theory tha t corresponds to general laws of motion. We plan to establish correspondence between Hamiltonian systems emerged in String Theory, evolutions equations in the plane, homogeneous and non-homogeneous groups and in adjacent topics of Harmonic and Geometric A nalysis.