Geometry, Education and Visualization With Applications

This project is a multidisciplinary project whose backbone is geometry and its various applications.Topics of project are:smooth manifolds and submanifolds endowed with different structures,their geometry and applications(gen. theory of relativity,cosmology,..);geometry and topology of fiber bundles;symmetric and homogeneous spaces,Lie groups and algebras and their actions;curvature(invariants,models,geom.realizability,..);in(ex)trinsic symmetries of (sub)manifolds,infinitesimal deformation of curves and surfaces;quantum groups;applications of p-adic,adelic methods in math. physics,biology and other complex systems;cosmological models;spectral theory of graphs;knots,links their applications;categorification of knot invariants and quantum groups;applications of math. methods in signal processing,computer graphics and control theory;random,stationary and stable processes;probabilistic methods in combinatorics;computing geom.,visualization of geom. objects and their applications in education;connection between empirical and theoretical knowledge in computer assisted teaching of geom.;development of existing and new software applicable in knot and graph theory.Expected results:obtaining new properties in mentioned topics and participation in development of corresponding theories,what will be verified by publishing obtained results in well-known international journals;development of old and new software and their applications;continuation of successful international cooperation.