Nilpotent Associative Algebras in Complex Geometry

This project concerns pure basic research in mathematics. It is centered around a recently discovered link between geometric objects called spherical tube hypersurfaces, and algebraic structures described as finite-dimensional nilpotent commutative associative algebras with 1-dimensional annihilator. Such algebras arise in particular from isolated hypersurface singularities, which are objects studied in the area of complex geometry. Hence there is a surprising relationship between spherical tube hypersurfaces and isolated hypersurface singularities, and the objectives of the project are: (1) to clarify the nature of this relationship, and (2) to utilise it for solving several significant problems involving spherical tube hypersurfaces.