Topology, geometry and global analysis on manifolds and discrete structures

The project is envisaged as one of the principal coordinators and carriers of multidisciplinary research in Serbia in the area of algebraic topology, differential geometry, global analysis, topological and geometric combinatorics and their applications in discrete and computational geometry and other areas. One of the goals of the project is to gather together different mathematical disciplines, each with its own techniques, around the same scientific project, focusing on the multidisciplinary study of geometric objects that appear in all of them. These include (symplectic, triangulated, Banach) manifolds, simplicial complexes etc., the objects which are at the center of virtually all methods for construction and analysis of geometric models in mathematics and its applications. The primary global effect of this multidisciplinary project is a creation of `critical mass’ of scientists for applications of complex techniques (equivariant topology, global analysis, symplectic and contact geometry) to problems of various structures on manifolds, problems of their realization in Euclidean spaces, problems of discretization of geometric objects (cellular structures, oriented matroids, partial orderings, discrete vector fields), etc. The secondary effect is the development of computational topology and discrete and computational geometry, as a vital connection of algebraic topology and geometric combinatorics with contemporary information technologies and applied mathematics.