Dear all, here is just a reminder that tomorrow Michiel Hochstenbach will give a seminar at SNS.
See you there! -- Leonardo.
On 3/6/19 11:34 AM, Leonardo Robol wrote:
Dear all, the next seminar will be the next week on Thursday (so _not_ tomorrow), and will be hosted at SNS. You find the abstract below.
See you there, Best, -- Leonardo.
Speaker: Michiel Hochstenbach Affiliation: TU Eindhoven Time: Thursday, 14 March 2019, h. 15:00 Place: Aula Tonelli, SNS
Title: Solving polynomial systems by determinantal representations
Zeros of a polynomial, p(x)=0, are often determined by computing the eigenvalues of a companion matrix: a matrix A which satisfies det(A-xI)=p(x). In this talk we consider polynomial systems, in particular in 2 variables: p(x,y)=0, q(x,y)=0. We look for a determinantal representation for such a bivariate polynomial: matrices A, B, C such that det(A-xB-yC)=p(x,y). This means that we can compute the zeros of the system by solving a 2-parameter eigenvalue problem. This approach, which already goes back to a theorem by Dixon in 1902, leads to fast solution methods, as well as a multitude of interesting open research questions.
This is mainly joint work with Bor Plestenjak (Ljubljana), and additionally several colleagues in algebra, among which Ada Boralevi (Torino).