From any given Frobenius manifold one may construct a so-called ‘dual’ structure which, while not satisfying the full axioms of a Frobenius manifold, shares many of its essential features, such as the existence of a prepotential satisfying the WDVV equations of associativity. Jacobi group orbit spaces naturally carry the structures of a Frobenius manifold and hence there exists a dual prepotent...

A finite dimensional Lie algebra f is Frobenius if there is a linear Frobenius functional F : f→ C such that the skew bilinear form BF defined by BF (x, y) = F ([x, y]) is non-degenerate. The principal element of f is then the unique element F̂ such that F (x) = F ([F̂ , x]); it depends on the choice of functional. However, if f is a subalgebra of a simple Lie algebra g and not an ideal of any la...

Overview. My work is in the area of commutative algebra, and is motivated by the connections between algebra and geometry. Commutative algebra is the study of commutative rings (e.g. polynomial rings over fields and their quotients) and modules over these rings, while algebraic geometry is the study of finitely many polynomial equations in finitely many unknowns. The set of all solutions to suc...