Jarod Alper: Associated forms in classical invariant theory

There is an interesting map which associates to a homogeneous form on C^n of degree d with non-vanishing discriminant, a form on C^n of degree n(d-2). This associated form can be identified with the Macaulay inverse system of the Milnor algebra of the original form.  It was conjectured in a recent paper by M. Eastword and A. Isaev that all absolute classical invariants of forms on C^n of degree d can be extracted from those of forms of degree n(d-2) via this map. This surprising conjecture was motivated by the well-known Mather-Yau theorem for isolated hypersurface singularities.  I will report on joint work with A. Isaev which settles this conjecture in full generality and proves a stronger statement in the case of binary forms.