The Principal Investigator intends to pursue two areas of research with the underlying theme of finding applications of topology to analysis and geometry. One theme is to study the homotopy properties of Kahler manifolds which fail for general symplectic manifolds. The relations between such properties will be explored. Related problem is to construct symplectic manifolds with prescribed homotopy properties. The other theme concerns topological methods in extremal problems. It involved estimates of the number of critical points of a function on a closed manifold using homotopy invariants.
The PI plans to continue his successful research in the area of topology, more specifically in homotopy theory. The above project can be regarded as the high level mathematics. Expected results make a real progress in homotopy theory, analysis and geometry and will stimulate further activity in these areas. Interdisciplinary character of the research will develop further interplay between different branches of mathematics. PI will disseminate results of his research and will be involved in training students.
