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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Degrees of the real Wronski maps

Presented by Andrei Gabrielov (Purdue) at 2.15 in CM 221,

16 May 2005 00:00 in CM221

"The Wronski map associates to a $p$-tuple of polynomials of degree $m+p-1$ their Wronski determinant, a polynomial of degree $mp$. If the polynomials are linearly independent, they define a a point in the Grassmannian $G(p,m+p)$. Accordingly, the Wronski map can be considered as a map from $G(p,m+p)$ to the projective space ${\bf P}^{mp}$. The map is finite, and one can define its degree. In the complex case, this degree equals the number of standard Young tableaux for the rectangular $(m,p)$-shape. In the real case, Young tableax should be counted with the signs depending on the number of inversions. Degree of the real Wronski map is zero when $m+p$ is even, and equals the number of standard shifted Young tableaux for an appropriately defined shifted shape when $m+p$ is odd. When both $m$ and $p$ are even, the Wronski map is not surjective. These results have important applications to real Schubert Calculus and to the pole placement problem in control theory. "

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