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20.11.2018

$“Associated forms: results and open problems”$

“Associated forms: results and open problems”

Alexander Isaev (The Australian National University, Canberra)

Chebyshev Laboratory Colloquium

Tuesday November 27, 17:15 room 14 (14-th line V.I., 29)

We discuss the morphism $\Phi$ , introduced by J. Alper, M. Eastwood and the speaker, that assigns to every non-degenerate homogeneous form of degree $d\ge 3$ in $n \ge 2$ variables the so-called associated form, which is a homogeneous form of degree $n(d-2)$ in $n$ variables. The morphism $\Phi$ is of interest in connection with the well-known Mather-Yau theorem, specifically, with the problem of the explicit reconstruction of an isolated hypersurface singularity from its Tjurina algebra. Furthermore, upon multiplication by a suitable power of the discriminant, the morphism leads to a previously unknown contravariant of homogeneous forms. In this talk, I will present a review of results and open problems related to $\Phi$ and the corresponding contravariant.