Equivalences and symmetries of k–nondegenerate CR manifolds

This project aims to address the equivalence problem for uniformly k-nondegenerate CR manifolds, a significant challenge in the field of differential geometry and complex analysis. The project will focus on developing new techniques to solve this problem by investigating normal forms, constructing models, and determining symmetries for these manifolds. The research will be conducted through a combination of Lie algebra methods, PDE analysis, and geometric constructions. Key objectives include: 1. Finding normal forms for real analytic uniformly 2-nondegenerate CR hypersurfaces. 2. Developing models for uniformly k-nondegenerate CR hypersurfaces for k greater than 2. 3. Realizing particular invariants and determining maximally symmetric realizations. 4. Solving the equivalence problem for k-nondegenerate CR hypersurfaces using the developed models. The project will involve national and international collaborations with experts in CR geometry, differential geometry, and complex analysis. The anticipated outcomes include high-quality publications in open-access journals and advancements in the understanding of CR manifolds` equivalence and symmetry properties.