Michael Penkava: Decomposition of moduli spaces of algebras using a stratification of the moduli space of matrices under scalar similarity and bilinear forms

In this talk I will discuss a certain stratification of the space of matrices under scalar symmetry by strata consisting of projective orbifolds
of a simple type,  that is $P^n/G$ where $G$ is a subgroup of the symmetric group $\Sigma_{n+1}$ which acts on $P^n$ by permuting the projective
coordinates.  It turns out that this stratification is the correct one from the deformation theory point of view, in the sense that elements of
a higher strata only deform along their own strata or jump to another strata.   In addition, I will discuss a stratification of the space of complex
bilinear forms under the cogredient action for low dimensions, which also plays a role in the decomposition of complex algebras into strata
of the same type.