[Aalto AGC Seminar] Etna Lindy | Partial multiplicities of the eigenvalues of the Sylvester resultant matrix | Mon 27.4. at 14:15

[Aalto Algebra, Geometry and Combinatorics Seminar]

We would like to invite you to the next talk of the spring in the Aalto AGC (Algebra, Geometry and Combinatorics) Seminar!

The talk is on
Mon 27.4. at 14:15-15:00
in
M3, Otakaari 1

The speaker is Etna Lindy

Title: Partial multiplicities of the eigenvalues of the Sylvester resultant matrix

Abstract: Resultant matrices are polynomial matrices associated to a system of polynomials such that the coordinates of the roots of the system are eigenvalues of the matrix.
In this talk, we will consider the bivariate case with two polynomials possibly sharing a multiple root.
It is known that the algebraic multiplicity of the eigenvalue corresponds to the multiplicity of the root.
In our work, we refine the connection between the multiplicities further; the partial multiplicities of the eigenvalues can be determined from the shape of the dual vector space of the ideal. The challenging part that has not been treated in the literature earlier concerns the possible roots at infinity, to which we give a complete treatment via Möbius transformations.


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