Geometric partial differential systems and their applications (2009-2011)
Abstract
The study of geometric analysis is now one of the main areas of modern mathematics, with diverse applications in physics and other sciences. We will investigate several important fundamental problems on geometric partial differential systems between mathematics and physics. Specific aims of the project are to investigate mathematical foundations of the heat flow approach in the Faddeev model, to provide solutions of unresolved conjectures on the Yang-Mills heat flow, and to develop the mathematical theory of liquid crystals. The expected outcomes are significant, fundamental results in mathematics, with applications in physics and other sciences.
